Statistics/Chi-squared distribution: Difference between revisions

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=={{header|Phix}}==
=={{header|Phix}}==
{{trans|Julia}}
{{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;">--
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\Chi-squared_distribution.exw
-- demo\rosetta\Chi-squared_distribution.exw
--</span>
--</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>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<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>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
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<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;">" ------------------------------------ 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: #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: #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>
<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>
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------------------------------------ Chi-squared ------------------------------------
------------------------------------ Chi-squared ------------------------------------
x k = 1 k = 2 k = 3 k = 4 k = 5
x k = 1 k = 2 k = 3 k = 4 k = 5
---------------------------------------------------------------------------------------------
--------------------------------------------------------------------------------------------
0 0.00000000000 0.00000000000 0.00000000000 0.00000000000 0.00000000000
0 0.00000000000 0.00000000000 0.00000000000 0.00000000000 0.00000000000
1 0.24197072452 0.30326532986 0.24197072452 0.15163266493 0.08065690817
1 0.24197072452 0.30326532986 0.24197072452 0.15163266493 0.08065690817
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Chi_squared x P value (df=3)
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,
For the airport data, diff total is 4.512820512820513,
degrees of freedom is 3,
degrees of freedom is 3,
ch-squared is 0.088753925984435,
ch-squared is 0.088753925984435,
p value is 0.788850426319306
p value is 0.788850426319307
</pre>
</pre>
[[File:Phixplotchisquared.png|thumb|center]]
[[File:Phixplotchisquared.png|thumb|center]]