Statistics/Chi-squared distribution: Difference between revisions

Line 188:

=={{header|Phix}}==

⚫

You can run this online [http://phix.x10.mx/p2js/chisqd.htm here].

⚫

--

-- demo\rosetta\Chi-squared_distribution.exw

--

~~without~~ ~~js -- mpfr_gamma[_inc]()~~

with javascript_semantics

~~requires~~(~~"1.0.2"~~) ~~-- mpfr_gamma_inc(~~)

function gamma(atom z)

~~include~~ ~~mpfr~~.e

constant p = { 0.99999999999980993,

676.5203681218851,

~~<span~~ ~~style="color:~~ ~~#008080;">function~~ ~~<span~~ ~~style="color:~~ ~~#000000;">gamma<span~~ ~~style="color:~~ ~~#0000FF;">(~~~~atom~~ x)

-1259.1392167224028,

~~-- gamma function for x~~, ~~using the MPFR library~~

771.32342877765313,

~~<span~~ ~~style="color:~~ ~~#004080;">mpfr~~ ~~<span~~ ~~style="color:~~ ~~#0000FF;">{<span~~ ~~style="color:~~ ~~#000000;">z<span~~ ~~style="color:~~ ~~#0000FF;">,~~ ~~<span~~ ~~style="color:~~ ~~#000000;">bigx<span~~ ~~style="color: #0000FF;">}~~ ~~= mpfr_inits(~~2,{~~<span~~ ~~style="color:~~ ~~#000000;">0,x})~~

-176.61502916214059,

~~<span~~ ~~style="color:~~ ~~#7060A8;">mpfr_gamma<span~~ ~~style="color:~~ ~~#0000FF;">(<span~~ ~~style="color:~~ ~~#000000;">z<span~~ ~~style="color:~~ ~~#0000FF;">,~~ ~~<span~~ ~~style="color:~~ ~~#000000;">bigx<span~~ ~~style="color:~~ ~~#0000FF;">,~~ 0)

12.507343278686905,

~~<span~~ ~~style="color:~~ ~~#008080;">return~~ ~~<span~~ ~~style="color:~~ ~~#7060A8;">mpfr_get_d~~(z)

-0.13857109526572012,

9.9843695780195716e-6,

1.5056327351493116e-7 }

if z<0.5 then

return PI / (sin(PI*z)*gamma(1-z))

end if

z -= 1;

atom x := p[1];

for i=1 to length(p)-1 do x += p[i+1]/(z+i) end for

atom t = z + length(p) - 1.5;

return sqrt(2*PI) * power(t,z+0.5) * exp(-t) * x

end function

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end function

function gamma_cdf(atom a, x)

function gamma_cdf(atom k, x)

-- ~~gamma CDF from~~ lower incomplete gamma ~~function,~~ ~~using~~ ~~MPFR~~ ~~library to get upper incomplete~~ gamma

-- lower incomplete gamma by series formula with gamma

~~mpfr~~ ~~{~~~~z,~~ ~~biga~~~~, bigx}~~ = mpfr_inits(3,{0~~,a,x})~~

atom tot = 0

~~mpfr_gamma_inc~~~~<span~~ ~~style="color: #0000FF;">(~~z, ~~biga~~, ~~bigx,~~ 0)

for m=0 to 100 do

~~return~~ 1-~~mpfr_get_d~~(z)/gamma(a)

tot += power(x,m) / gamma(k + m + 1)

end for

return power(x,k) * exp(-x) * tot

end function

Line 222:

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printf(1," ------------------------------------ Chi-squared ------------------------------------\n")

printf(1," x k = 1 k = 2 k = 3 k = 4 k = 5\n")

printf(1,repeat('-',93)&"\n")

printf(1,repeat('-',92)&"\n")

for x=0 to 10 do

printf(1,"%2d",x)

Line 280:

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------------------------------------ Chi-squared ------------------------------------

x k = 1 k = 2 k = 3 k = 4 k = 5

---------------------------------------------------------------------------------------------

--------------------------------------------------------------------------------------------

0 0.00000000000 0.00000000000 0.00000000000 0.00000000000 0.00000000000

1 0.24197072452 0.30326532986 0.24197072452 0.15163266493 0.08065690817

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Chi_squared x P value (df=3)

------------------------------------

1 0.~~8012519569012008~~

1 0.8012519569012007

2 0.~~5724067044708798~~

2 0.5724067044708797

4 0.~~2614641299491106~~

4 0.2614641299491101

8 0.~~0460117056892314~~

8 0.0460117056892316

16 0.~~0011339842897853~~

16 0.0011339842897863

32 5.~~233466447984724e~~-7

32 5.233466446874501e-7

For the airport data, diff total is 4.512820512820513,

degrees of freedom is 3,

ch-squared is 0.088753925984435,

p value is 0.~~788850426319306~~

p value is 0.788850426319307

</pre>

[[File:Phixplotchisquared.png|thumb|center]]

@@ Line 188: / Line 188: @@
 =={{header|Phix}}==
 {{trans|Julia}}
+{{libheader|Phix/online}}
-<!--<syntaxhighlight lang="phix">(notonline)-->
+You can run this online [http://phix.x10.mx/p2js/chisqd.htm here].
+<!--<syntaxhighlight lang="phix">(phixonline)-->
  <span style="color: #000080;font-style:italic;">--
  -- demo\rosetta\Chi-squared_distribution.exw
  --</span>
- <span style="color: #008080;">without</span> <span style="color: #008080;">js</span>          <span style="color: #000080;font-style:italic;">-- mpfr_gamma[_inc]()</span>
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
- <span style="color: #7060A8;">requires</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"1.0.2"</span><span style="color: #0000FF;">)</span>   <span style="color: #000080;font-style:italic;">-- mpfr_gamma_inc()</span>
+ <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>
- <span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
+     <span style="color: #008080;">constant</span> <span style="color: #000000;">p</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span>   <span style="color: #000000;">0.99999999999980993</span><span style="color: #0000FF;">,</span>
+                    <span style="color: #000000;">676.5203681218851</span><span style="color: #0000FF;">,</span>
- <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;">x</span><span style="color: #0000FF;">)</span>
+                  <span style="color: #0000FF;">-</span><span style="color: #000000;">1259.1392167224028</span><span style="color: #0000FF;">,</span>
- <span style="color: #000080;font-style:italic;">-- gamma function for x, using the MPFR library</span>
+                    <span style="color: #000000;">771.32342877765313</span><span style="color: #0000FF;">,</span>
-     <span style="color: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bigx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">2</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: #0000FF;">-</span><span style="color: #000000;">176.61502916214059</span><span style="color: #0000FF;">,</span>
-     <span style="color: #7060A8;">mpfr_gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bigx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+                     <span style="color: #000000;">12.507343278686905</span><span style="color: #0000FF;">,</span>
-     <span style="color: #008080;">return</span> <span style="color: #7060A8;">mpfr_get_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)</span>
+                     <span style="color: #0000FF;">-</span><span style="color: #000000;">0.13857109526572012</span><span style="color: #0000FF;">,</span>
+                      <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>
+     <span style="color: #008080;">if</span> <span style="color: #000000;">z</span><span style="color: #0000FF;"><</span><span style="color: #000000;">0.5</span> <span style="color: #008080;">then</span>
+         <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;">z</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;">z</span><span style="color: #0000FF;">))</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+     <span style="color: #000000;">z</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">1</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;">1</span><span style="color: #0000FF;">];</span>
+     <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;">p</span><span style="color: #0000FF;">)-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</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;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]/(</span><span style="color: #000000;">z</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>
+     <span style="color: #004080;">atom</span> <span style="color: #000000;">t</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">z</span> <span style="color: #0000FF;">+</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: #0000FF;">-</span> <span style="color: #000000;">1.5</span><span style="color: #0000FF;">;</span>
+     <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;">z</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;">x</span>
  <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
@@ Line 208: / Line 220: @@
  <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
- <span style="color: #008080;">function</span> <span style="color: #000000;">gamma_cdf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">gamma_cdf</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
- <span style="color: #000080;font-style:italic;">-- gamma CDF from lower incomplete gamma function, using MPFR library to get upper incomplete gamma</span>
+ <span style="color: #000080;font-style:italic;">-- lower incomplete gamma by series formula with gamma</span>
-     <span style="color: #004080;">mpfr</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">biga</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bigx</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpfr_inits</span><span style="color: #0000FF;">(</span><span style="color: #000000;">3</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">})</span>
+     <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: #7060A8;">mpfr_gamma_inc</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">biga</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">bigx</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">100</span> <span style="color: #008080;">do</span>
-     <span style="color: #008080;">return</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">-</span><span style="color: #7060A8;">mpfr_get_d</span><span style="color: #0000FF;">(</span><span style="color: #000000;">z</span><span style="color: #0000FF;">)/</span><span style="color: #000000;">gamma</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">tot</span> <span style="color: #0000FF;">+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">m</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;">k</span> <span style="color: #0000FF;">+</span> <span style="color: #000000;">m</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;">return</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</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;">x</span><span style="color: #0000FF;">)</span> <span style="color: #0000FF;">*</span> <span style="color: #000000;">tot</span>
  <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
@@ Line 222: / Line 236: @@
  <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"       ------------------------------------ Chi-squared ------------------------------------\n"</span><span style="color: #0000FF;">)</span>
  <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">" x             k = 1             k = 2             k = 3             k = 4             k = 5\n"</span><span style="color: #0000FF;">)</span>
- <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">93</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
+ <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'-'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">92</span><span style="color: #0000FF;">)&</span><span style="color: #008000;">"\n"</span><span style="color: #0000FF;">)</span>
  <span style="color: #008080;">for</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
      <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%2d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
@@ Line 280: / Line 294: @@
        ------------------------------------ Chi-squared ------------------------------------
  x             k = 1             k = 2             k = 3             k = 4             k = 5
----------------------------------------------------------------------------------------------
+--------------------------------------------------------------------------------------------
 0.00000000000     0.00000000000     0.00000000000     0.00000000000     0.00000000000
 0.24197072452     0.30326532986     0.24197072452     0.15163266493     0.08065690817
@@ Line 295: / Line 309: @@
 Chi_squared x     P value (df=3)
 ------------------------------------
-0.8012519569012008
+0.8012519569012007
-0.5724067044708798
+0.5724067044708797
-0.2614641299491106
+0.2614641299491101
-0.0460117056892314
+0.0460117056892316
-0.0011339842897853
+0.0011339842897863
-5.233466447984724e-7
+5.233466446874501e-7
 For the airport data, diff total is 4.512820512820513,
               degrees of freedom is 3,
                       ch-squared is 0.088753925984435,
-                         p value is 0.788850426319306
+                         p value is 0.788850426319307
 </pre>
 [[File:Phixplotchisquared.png|thumb|center]]