Welch's t-test: Difference between revisions
Content added Content deleted
m (→{{header|Phix}}: syntax coloured) |
|||
Line 1,347: | Line 1,347: | ||
{{trans|Go}} |
{{trans|Go}} |
||
{{trans|Kotlin}} |
{{trans|Kotlin}} |
||
<lang Phix> |
<!--<lang Phix>(phixonline)--> |
||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
|||
return sum(a) / length(a) |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function sv(sequence a) |
|||
integer la = length(a) |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">sv</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> |
|||
atom m := mean(a), |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> |
|||
tot := 0 |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">m</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> |
|||
for i=1 to la do |
|||
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">0</span> |
|||
atom d = a[i] - m |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">la</span> <span style="color: #008080;">do</span> |
|||
tot += d * d |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">m</span> |
|||
end for |
|||
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">d</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">d</span> |
|||
return tot / (la-1) |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function welch(sequence a, b) |
|||
integer la = length(a), |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">welch</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
|||
lb = length(b) |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> |
|||
return (mean(a) - mean(b)) / sqrt(sv(a)/la+sv(b)/lb) |
|||
<span style="color: #000000;">lb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">mean</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;">/</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">sv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">la</span><span style="color: #0000FF;">+</span><span style="color: #000000;">sv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function dof(sequence a, b) |
|||
integer la = length(a), |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">dof</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
|||
lb = length(b) |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> |
|||
atom sva := sv(a), |
|||
<span style="color: #000000;">lb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
|||
svb := sv(b), |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">sva</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">sv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> |
|||
n := sva/la + svb/lb |
|||
<span style="color: #000000;">svb</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">sv</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">),</span> |
|||
return n * n / (sva*sva/(la*la*(la-1)) + |
|||
<span style="color: #000000;">n</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">sva</span><span style="color: #0000FF;">/</span><span style="color: #000000;">la</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">svb</span><span style="color: #0000FF;">/</span><span style="color: #000000;">lb</span> |
|||
svb*svb/(lb*lb*(lb-1))) |
|||
<span style="color: #008080;">return</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">sva</span><span style="color: #0000FF;">*</span><span style="color: #000000;">sva</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">*</span><span style="color: #000000;">la</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;">+</span> |
|||
end function |
|||
<span style="color: #000000;">svb</span><span style="color: #0000FF;">*</span><span style="color: #000000;">svb</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">*</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)))</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function f(atom r, v) |
|||
return power(r, v/2-1) / sqrt(1-r) |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function simpson0(integer n, atom high, v) |
|||
atom tot := 0, |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">simpson0</span><span style="color: #0000FF;">(</span><span style="color: #004080;">integer</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">atom</span> <span style="color: #000000;">high</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> |
|||
dx0 := high / n, |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">tot</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> |
|||
x0 := dx0, x1, xmid, dx |
|||
<span style="color: #000000;">dx0</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">high</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">,</span> |
|||
tot += f(0,v) * dx0 |
|||
<span style="color: #000000;">x0</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">dx0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">xmid</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dx</span> |
|||
tot += f(dx0*.5,v) * dx0 * 4 |
|||
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">dx0</span> |
|||
for i=1 to n-1 do |
|||
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">dx0</span><span style="color: #0000FF;">*.</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">dx0</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">4</span> |
|||
x1 := (i+1) * high / n |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span> |
|||
xmid := (x0 + x1) * .5 |
|||
<span style="color: #000000;">x1</span> <span style="color: #0000FF;">:=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">high</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">n</span> |
|||
dx := x1 - x0 |
|||
<span style="color: #000000;">xmid</span> <span style="color: #0000FF;">:=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">x0</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">x1</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #0000FF;">.</span><span style="color: #000000;">5</span> |
|||
tot += f(x0,v) * dx * 2 |
|||
<span style="color: #000000;">dx</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">x1</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">x0</span> |
|||
tot += f(xmid,v) * dx * 4 |
|||
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">dx</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">2</span> |
|||
x0 = x1 |
|||
<span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">xmid</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">dx</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">4</span> |
|||
end for |
|||
<span style="color: #000000;">x0</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x1</span> |
|||
return (tot + f(high,v)*dx0) / 6 |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">tot</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">f</span><span style="color: #0000FF;">(</span><span style="color: #000000;">high</span><span style="color: #0000FF;">,</span><span style="color: #000000;">v</span><span style="color: #0000FF;">)*</span><span style="color: #000000;">dx0</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">6</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
constant p = { |
|||
0.99999999999980993, |
|||
<span style="color: #008080;">constant</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span> |
|||
676.5203681218851, |
|||
<span style="color: #000000;">0.99999999999980993</span><span style="color: #0000FF;">,</span> |
|||
-1259.1392167224028, |
|||
<span style="color: #000000;">676.5203681218851</span><span style="color: #0000FF;">,</span> |
|||
771.32342877765313, |
|||
<span style="color: #0000FF;">-</span><span style="color: #000000;">1259.1392167224028</span><span style="color: #0000FF;">,</span> |
|||
-176.61502916214059, |
|||
<span style="color: #000000;">771.32342877765313</span><span style="color: #0000FF;">,</span> |
|||
12.507343278686905, |
|||
<span style="color: #0000FF;">-</span><span style="color: #000000;">176.61502916214059</span><span style="color: #0000FF;">,</span> |
|||
-0.13857109526572012, |
|||
<span style="color: #000000;">12.507343278686905</span><span style="color: #0000FF;">,</span> |
|||
9.9843695780195716e-6, |
|||
<span style="color: #0000FF;">-</span><span style="color: #000000;">0.13857109526572012</span><span style="color: #0000FF;">,</span> |
|||
1.5056327351493116e-7 |
|||
<span style="color: #000000;">9.9843695780195716e-6</span><span style="color: #0000FF;">,</span> |
|||
} |
|||
<span style="color: #000000;">1.5056327351493116e-7</span> |
|||
<span style="color: #0000FF;">}</span> |
|||
function gamma(atom d) |
|||
atom dd = d, |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> |
|||
g = 7 |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">dd</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">,</span> |
|||
if dd<0.5 then |
|||
<span style="color: #000000;">g</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">7</span> |
|||
return PI / (sin(PI*dd) * gamma(1-dd)) |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">dd</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0.5</span> <span style="color: #008080;">then</span> |
|||
end if |
|||
<span style="color: #008080;">return</span> <span style="color: #004600;">PI</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #7060A8;">sin</span><span style="color: #0000FF;">(</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">*</span><span style="color: #000000;">dd</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">dd</span><span style="color: #0000FF;">))</span> |
|||
dd -= 1 |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
atom a = p[1], |
|||
<span style="color: #000000;">dd</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span> |
|||
t = dd + g + 0.5 |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">],</span> |
|||
for i=2 to length(p) do a += p[i] / (dd + i - 1) end for |
|||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">dd</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">g</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">0.5</span> |
|||
return sqrt(2*PI) * power(t, dd + 0.5) * exp(-t) * a |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">dd</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">i</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">dd</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-</span><span style="color: #000000;">t</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">a</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function lGamma(atom d) |
|||
return log(gamma(d)) |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">lGamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">))</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
function pValue(sequence ab) |
|||
sequence {a, b} = ab |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">pValue</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">ab</span><span style="color: #0000FF;">)</span> |
|||
atom v := dof(a, b), |
|||
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ab</span> |
|||
t := welch(a, b), |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">v</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">dof</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">),</span> |
|||
g1 := lGamma(v / 2), |
|||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">welch</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">),</span> |
|||
g2 := lGamma(.5), |
|||
<span style="color: #000000;">g1</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">lGamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">),</span> |
|||
g3 := lGamma(v/2 + .5) |
|||
<span style="color: #000000;">g2</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">lGamma</span><span style="color: #0000FF;">(.</span><span style="color: #000000;">5</span><span style="color: #0000FF;">),</span> |
|||
return simpson0(2000, v/(t*t+v), v) / exp(g1+g2-g3) |
|||
<span style="color: #000000;">g3</span> <span style="color: #0000FF;">:=</span> <span style="color: #000000;">lGamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">v</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">.</span><span style="color: #000000;">5</span><span style="color: #0000FF;">)</span> |
|||
end function |
|||
<span style="color: #008080;">return</span> <span style="color: #000000;">simpson0</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2000</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">v</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">v</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">g1</span><span style="color: #0000FF;">+</span><span style="color: #000000;">g2</span><span style="color: #0000FF;">-</span><span style="color: #000000;">g3</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
constant tests = {{{27.5, 21.0, 19.0, 23.6, 17.0, 17.9, 16.9, 20.1, 21.9, 22.6, 23.1, 19.6, 19.0, 21.7, 21.4}, |
|||
{27.1, 22.0, 20.8, 23.4, 23.4, 23.5, 25.8, 22.0, 24.8, 20.2, 21.9, 22.1, 22.9, 20.5, 24.4}}, |
|||
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{</span><span style="color: #000000;">27.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">16.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.4</span><span style="color: #0000FF;">},</span> |
|||
{{17.2, 20.9, 22.6, 18.1, 21.7, 21.4, 23.5, 24.2, 14.7, 21.8}, |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">27.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.4</span><span style="color: #0000FF;">}},</span> |
|||
{21.5, 22.8, 21.0, 23.0, 21.6, 23.6, 22.5, 20.7, 23.4, 21.8, 20.7, 21.7, 21.5, 22.5, 23.6, 21.5, 22.5, 23.5, 21.5, 21.8}}, |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">17.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.8</span><span style="color: #0000FF;">},</span> |
|||
{{19.8, 20.4, 19.6, 17.8, 18.5, 18.9, 18.3, 18.9, 19.5, 22.0}, |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.8</span><span style="color: #0000FF;">}},</span> |
|||
{28.2, 26.6, 20.1, 23.3, 25.2, 22.1, 17.7, 27.6, 20.6, 13.7, 23.2, 17.5, 20.6, 18.0, 23.9, 21.6, 24.3, 20.4, 24.0, 13.2}}, |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">19.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.0</span><span style="color: #0000FF;">},</span> |
|||
{{30.02, 29.99, 30.11, 29.97, 30.01, 29.99}, |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">28.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">26.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">27.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">13.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">13.2</span><span style="color: #0000FF;">}},</span> |
|||
{29.89, 29.93, 29.72, 29.98, 30.02, 29.98}}, |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">30.02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.99</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30.11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.97</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30.01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.99</span><span style="color: #0000FF;">},</span> |
|||
{{3.0, 4.0, 1.0, 2.1}, |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">29.89</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.93</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.72</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.98</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30.02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.98</span><span style="color: #0000FF;">}},</span> |
|||
{490.2, 340.0, 433.9}} |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">3.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.1</span><span style="color: #0000FF;">},</span> |
|||
} |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">490.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">340.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">433.9</span><span style="color: #0000FF;">}}</span> |
|||
<span style="color: #0000FF;">}</span> |
|||
for i=1 to length(tests) do |
|||
?pValue(tests[i]) |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
|||
end for</lang> |
|||
<span style="color: #0000FF;">?</span><span style="color: #000000;">pValue</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
<!--</lang>--> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
0.0213780015 |
|||
0.02137800146 |
|||
0.1488416966 |
0.1488416966 |
||
0.035972271 |
|||
0.03597227103 |
|||
0.0907733243 |
|||
0.09077332429 |
|||
0.0107506737 |
|||
0.01075067374 |
|||
</pre> |
</pre> |
||
{{trans|Python}} |
{{trans|Python}} |
||
The above was a bit off on the fifth test, so I also tried this.<br> |
The above was a bit off on the fifth test, so I also tried this.<br> |
||
using gamma() from [[Gamma_function#Phix]] (the one from above is probably also fine, but I didn't test that) |
using gamma() from [[Gamma_function#Phix]] (the one from above is probably also fine, but I didn't test that) |
||
<lang Phix> |
<!--<lang Phix>(phixonline)--> |
||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span> |
|||
return log(gamma(d)) |
|||
<span style="color: #000080;font-style:italic;">--<copy of gamma from Gamma_function#Phix></span> |
|||
end function |
|||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">12</span><span style="color: #0000FF;">)</span> |
|||
function betain(atom x, p, q) |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">gamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">z</span><span style="color: #0000FF;">)</span> |
|||
if p<=0 or q<=0 or x<0 or x>1 then ?9/0 end if |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> |
|||
if x == 0 or x == 1 then return x end if |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">accm</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
|||
<span style="color: #000000;">accm</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #004600;">PI</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">accm</span> |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span> <span style="color: #000080;font-style:italic;">-- (k - 1)!*(-1)^k with 0!==1</span> |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span> |
|||
<span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">13</span><span style="color: #0000FF;">-</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1.5</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">k1_factrl</span> |
|||
<span style="color: #000000;">k1_factrl</span> <span style="color: #0000FF;">*=</span> <span style="color: #0000FF;">-(</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">=</span><span style="color: #000000;">2</span> <span style="color: #008080;">to</span> <span style="color: #000000;">12</span> <span style="color: #008080;">do</span> |
|||
<span style="color: #000000;">accm</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">[</span><span style="color: #000000;">k</span><span style="color: #0000FF;">]/(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">k</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
<span style="color: #000000;">accm</span> <span style="color: #0000FF;">*=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(-(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">))*</span><span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">12</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">+</span><span style="color: #000000;">0.5</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- Gamma(z+1)</span> |
|||
<span style="color: #008080;">return</span> <span style="color: #000000;">accm</span><span style="color: #0000FF;">/</span><span style="color: #000000;">z</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
<span style="color: #000080;font-style:italic;">--</copy of gamma></span> |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">lgamma</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">d</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">return</span> <span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">d</span><span style="color: #0000FF;">))</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">betain</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">p</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">p</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">q</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">></span><span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #0000FF;">?</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">or</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">1</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">x</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">acu</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1e-15</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">lnbeta</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lgamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">lgamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">lgamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">),</span> |
|||
<span style="color: #000000;">psq</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">q</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">cx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">x</span> |
|||
<span style="color: #004080;">bool</span> <span style="color: #000000;">indx</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;"><</span><span style="color: #000000;">psq</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">indx</span> <span style="color: #008080;">then</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">cx</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">q</span><span style="color: #0000FF;">,</span><span style="color: #000000;">p</span><span style="color: #0000FF;">}</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">term</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">ai</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">val</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">ns</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">floor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">q</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">cx</span><span style="color: #0000FF;">*</span><span style="color: #000000;">psq</span><span style="color: #0000FF;">),</span> |
|||
<span style="color: #000000;">rx</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ns</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">?</span><span style="color: #000000;">x</span><span style="color: #0000FF;">:</span><span style="color: #000000;">x</span><span style="color: #0000FF;">/</span><span style="color: #000000;">cx</span><span style="color: #0000FF;">),</span> |
|||
<span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">ai</span> |
|||
<span style="color: #008080;">while</span> <span style="color: #004600;">true</span> <span style="color: #008080;">do</span> |
|||
<span style="color: #000000;">term</span> <span style="color: #0000FF;">*=</span> <span style="color: #000000;">temp</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">rx</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">p</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">ai</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #000000;">val</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">term</span> |
|||
<span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">term</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">temp</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">acu</span> <span style="color: #008080;">and</span> <span style="color: #000000;">temp</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">acu</span><span style="color: #0000FF;">*</span><span style="color: #000000;">val</span> <span style="color: #008080;">then</span> |
|||
<span style="color: #000000;">val</span> <span style="color: #0000FF;">*=</span> <span style="color: #7060A8;">exp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">p</span><span style="color: #0000FF;">*</span><span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">+</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">q</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)*</span><span style="color: #7060A8;">log</span><span style="color: #0000FF;">(</span><span style="color: #000000;">cx</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">lnbeta</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #000000;">p</span> |
|||
<span style="color: #008080;">return</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #000000;">indx</span><span style="color: #0000FF;">?</span><span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #000000;">val</span><span style="color: #0000FF;">:</span><span style="color: #000000;">val</span><span style="color: #0000FF;">)</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #000000;">ai</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
|||
<span style="color: #000000;">ns</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</span> |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">ns</span><span style="color: #0000FF;">>=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
|||
<span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">q</span> <span style="color: #0000FF;">-</span> <span style="color: #000000;">ai</span> |
|||
<span style="color: #008080;">if</span> <span style="color: #000000;">ns</span> <span style="color: #0000FF;">==</span> <span style="color: #000000;">0</span> <span style="color: #008080;">then</span> |
|||
<span style="color: #000000;">rx</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #008080;">else</span> |
|||
<span style="color: #000000;">temp</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">psq</span> |
|||
<span style="color: #000000;">psq</span> <span style="color: #0000FF;">+=</span> <span style="color: #000000;">1</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
<span style="color: #008080;">function</span> <span style="color: #000000;">welch_ttest</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">ab</span><span style="color: #0000FF;">)</span> |
|||
atom acu = 1e-15, |
|||
<span style="color: #004080;">sequence</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ab</span> |
|||
lnbeta = lgamma(p) + lgamma(q) - lgamma(p + q), |
|||
<span style="color: #004080;">integer</span> <span style="color: #000000;">la</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">),</span> |
|||
psq = p + q, cx = 1-x |
|||
<span style="color: #000000;">lb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> |
|||
bool indx = (p<psq*x) |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">ma</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">la</span><span style="color: #0000FF;">,</span> |
|||
if indx then |
|||
<span style="color: #000000;">mb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">,</span> |
|||
{cx,x,p,q} = {x,1-x,q,p} |
|||
<span style="color: #000000;">va</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_power</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">ma</span><span style="color: #0000FF;">),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))/(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> |
|||
end if |
|||
<span style="color: #000000;">vb</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sum</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_power</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">,</span><span style="color: #000000;">mb</span><span style="color: #0000FF;">),</span><span style="color: #000000;">2</span><span style="color: #0000FF;">))/(</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">),</span> |
|||
<span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">va</span><span style="color: #0000FF;">/</span><span style="color: #000000;">la</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">vb</span><span style="color: #0000FF;">/</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">,</span> |
|||
atom term = 1, |
|||
<span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">ma</span><span style="color: #0000FF;">-</span><span style="color: #000000;">mb</span><span style="color: #0000FF;">)/</span><span style="color: #7060A8;">sqrt</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span> |
|||
ai = 1, |
|||
<span style="color: #000000;">df</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">*</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">/</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">va</span><span style="color: #0000FF;">*</span><span style="color: #000000;">va</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">*</span><span style="color: #000000;">la</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">la</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">))</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">vb</span><span style="color: #0000FF;">*</span><span style="color: #000000;">vb</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">*</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">lb</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)))</span> |
|||
val = 1, |
|||
<span style="color: #008080;">return</span> <span style="color: #000000;">betain</span><span style="color: #0000FF;">(</span><span style="color: #000000;">df</span><span style="color: #0000FF;">/(</span><span style="color: #000000;">t</span><span style="color: #0000FF;">*</span><span style="color: #000000;">t</span><span style="color: #0000FF;">+</span><span style="color: #000000;">df</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">df</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">/</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span> |
|||
ns = floor(q + cx*psq), |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span> |
|||
rx = iff(ns=0?x:x/cx), |
|||
temp = q - ai |
|||
<span style="color: #008080;">constant</span> <span style="color: #000000;">tests</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{{</span><span style="color: #000000;">27.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">16.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.4</span><span style="color: #0000FF;">},</span> |
|||
while true do |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">27.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.4</span><span style="color: #0000FF;">}},</span> |
|||
term *= temp * rx / (p + ai) |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">17.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">14.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.8</span><span style="color: #0000FF;">},</span> |
|||
val += term |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.8</span><span style="color: #0000FF;">}},</span> |
|||
temp = abs(term) |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">19.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.8</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">19.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.0</span><span style="color: #0000FF;">},</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">28.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">26.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">25.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">22.1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">27.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">13.7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">17.5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">18.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">23.9</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">21.6</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">20.4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">24.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">13.2</span><span style="color: #0000FF;">}},</span> |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">30.02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.99</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30.11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.97</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30.01</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.99</span><span style="color: #0000FF;">},</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">29.89</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.93</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.72</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.98</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">30.02</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">29.98</span><span style="color: #0000FF;">}},</span> |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">3.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">4.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2.1</span><span style="color: #0000FF;">},</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">490.2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">340.0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">433.9</span><span style="color: #0000FF;">}},</span> |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">0.010268</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.000167</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.000167</span><span style="color: #0000FF;">},</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">0.159258</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.136278</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0.122389</span><span style="color: #0000FF;">}},</span> |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">1.0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">15</span><span style="color: #0000FF;">,</span><span style="color: #000000;">10.0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">62.0</span><span style="color: #0000FF;">},</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">1.0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">10</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">/</span><span style="color: #000000;">50.0</span><span style="color: #0000FF;">}},</span> |
|||
<span style="color: #0000FF;">{{</span><span style="color: #000000;">9</span><span style="color: #0000FF;">/</span><span style="color: #000000;">23.0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">21</span><span style="color: #0000FF;">/</span><span style="color: #000000;">45.0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">38.0</span><span style="color: #0000FF;">},</span> |
|||
<span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">44.0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">42</span><span style="color: #0000FF;">/</span><span style="color: #000000;">94.0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">/</span><span style="color: #000000;">22.0</span><span style="color: #0000FF;">}}},</span> |
|||
<span style="color: #000000;">correct</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0.021378001462867</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.148841696605327</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.0359722710297968</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.090773324285671</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.0107515611497845</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.00339907162713746</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.52726574965384</span><span style="color: #0000FF;">,</span> |
|||
<span style="color: #000000;">0.545266866977794</span><span style="color: #0000FF;">}</span> |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">cerr</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span> |
|||
if temp<=acu and temp<=acu*val then |
|||
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> |
|||
val *= exp(p*log(x) + (q-1)*log(cx) - lnbeta) / p |
|||
<span style="color: #004080;">atom</span> <span style="color: #000000;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">welch_ttest</span><span style="color: #0000FF;">(</span><span style="color: #000000;">tests</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
|||
return iff(indx?1-val:val) |
|||
<span style="color: #0000FF;">?</span><span style="color: #000000;">r</span> |
|||
end if |
|||
<span style="color: #000000;">cerr</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">abs</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">-</span><span style="color: #000000;">correct</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> |
|||
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span> |
|||
ai += 1 |
|||
<span style="color: #0000FF;">?{</span><span style="color: #008000;">"cumulative error"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">cerr</span><span style="color: #0000FF;">}</span> |
|||
ns -= 1 |
|||
<!--</lang>--> |
|||
if ns>=0 then |
|||
temp = q - ai |
|||
if ns == 0 then |
|||
rx = x |
|||
end if |
|||
else |
|||
temp = psq |
|||
psq += 1 |
|||
end if |
|||
end while |
|||
end function |
|||
function welch_ttest(sequence ab) |
|||
sequence {a, b} = ab |
|||
integer la = length(a), |
|||
lb = length(b) |
|||
atom ma = sum(a)/la, |
|||
mb = sum(b)/lb, |
|||
va = sum(sq_power(sq_sub(a,ma),2))/(la-1), |
|||
vb = sum(sq_power(sq_sub(b,mb),2))/(lb-1), |
|||
n = va/la + vb/lb, |
|||
t = (ma-mb)/sqrt(n), |
|||
df = (n*n) / (va*va/(la*la*(la-1)) + vb*vb/(lb*lb*(lb-1))) |
|||
return betain(df/(t*t+df), df/2, 1/2) |
|||
end function |
|||
constant tests = {{{27.5, 21.0, 19.0, 23.6, 17.0, 17.9, 16.9, 20.1, 21.9, 22.6, 23.1, 19.6, 19.0, 21.7, 21.4}, |
|||
{27.1, 22.0, 20.8, 23.4, 23.4, 23.5, 25.8, 22.0, 24.8, 20.2, 21.9, 22.1, 22.9, 20.5, 24.4}}, |
|||
{{17.2, 20.9, 22.6, 18.1, 21.7, 21.4, 23.5, 24.2, 14.7, 21.8}, |
|||
{21.5, 22.8, 21.0, 23.0, 21.6, 23.6, 22.5, 20.7, 23.4, 21.8, 20.7, 21.7, 21.5, 22.5, 23.6, 21.5, 22.5, 23.5, 21.5, 21.8}}, |
|||
{{19.8, 20.4, 19.6, 17.8, 18.5, 18.9, 18.3, 18.9, 19.5, 22.0}, |
|||
{28.2, 26.6, 20.1, 23.3, 25.2, 22.1, 17.7, 27.6, 20.6, 13.7, 23.2, 17.5, 20.6, 18.0, 23.9, 21.6, 24.3, 20.4, 24.0, 13.2}}, |
|||
{{30.02, 29.99, 30.11, 29.97, 30.01, 29.99}, |
|||
{29.89, 29.93, 29.72, 29.98, 30.02, 29.98}}, |
|||
{{3.0, 4.0, 1.0, 2.1}, |
|||
{490.2, 340.0, 433.9}}, |
|||
{{0.010268,0.000167,0.000167}, |
|||
{0.159258,0.136278,0.122389}}, |
|||
{{1.0/15,10.0/62.0}, |
|||
{1.0/10,2/50.0}}, |
|||
{{9/23.0,21/45.0,0/38.0}, |
|||
{0/44.0,42/94.0,0/22.0}}}, |
|||
correct = {0.021378001462867, |
|||
0.148841696605327, |
|||
0.0359722710297968, |
|||
0.090773324285671, |
|||
0.0107515611497845, |
|||
0.00339907162713746, |
|||
0.52726574965384, |
|||
0.545266866977794} |
|||
atom cerr = 0 |
|||
for i=1 to length(tests) do |
|||
atom r = welch_ttest(tests[i]) |
|||
?r |
|||
cerr += abs(r-correct[i]) |
|||
end for |
|||
?{"cumulative error",cerr}</lang> |
|||
{{out}} |
{{out}} |
||
<pre> |
<pre> |
||
Line 1,567: | Line 1,595: | ||
0.5272657497 |
0.5272657497 |
||
0.545266867 |
0.545266867 |
||
{"cumulative error",1.989380882e-14} -- (32 bit) |
{"cumulative error",1.989380882e-14} -- (32 bit/p2js) |
||
{"cumulative error",4.915115776e-15} -- (64-bit) |
{"cumulative error",4.915115776e-15} -- (64-bit) |
||
</pre> |
</pre> |