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Statistics/Chi-squared distribution (view source)

Revision as of 12:12, 3 October 2022

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=={{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">(notonlinephixonline)-->
<span style="color: #000080;font-style:italic;">--
-- demo\rosetta\Chi-squared_distribution.exw
--</span>
<span style="color: #008080;">withoutwith</span> <span style="color: #008080;">js</span> <span style="color: #000080;font-style:italic;">-- mpfr_gamma[_inc]()javascript_semantics</span>
<span style="color: #7060A8008080;">requiresfunction</span> <span style="color: #0000FF000000;">(gamma</span><span style="color: #0080000000FF;">"1.0.2"(</span><span style="color: #0000FF004080;">)atom</span> <span style="color: #000080000000;font-">z</span><span style="color:italic #0000FF;">-- mpfr_gamma_inc()</span>
<span style="color: #008080;">includeconstant</span> <span style="color: #004080000000;">mpfrp</span> <span style="color: #0000FF;">.=</span> <span style="color: #0000FF;">{</span> <span style="color: #000000;">e0.99999999999980993</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: #0040800000FF;">atom-</span> <span style="color: #000000;">x1259.1392167224028</span><span style="color: #0000FF;">),</span>
<span style="color: #000080000000;font-">771.32342877765313</span><span style="color:italic #0000FF;">-- gamma function for x, using the MPFR library</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;">2176.61502916214059</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: #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;">012.507343278686905</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;">z0.13857109526572012</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>
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<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;">ak</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,by usingseries MPFRformula library to get upper incompletewith gamma</span>
<span style="color: #004080;">mpfratom</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">z</span><span style="color: #0000FF;">,tot</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: #7060A8008080;">mpfr_gamma_incfor</span><span style="color: #0000FF;">(</span><span style="color: #000000;">zm</span><span style="color: #0000FF;">,=</span> <span style="color: #000000;">biga0</span> <span style="color: #0000FF008080;">,to</span> <span style="color: #000000;">bigx</span><span style="color: #0000FF;">,100</span> <span style="color: #000000;">0</span><span style="color: #0000FF008080;">)do</span>
<span style="color: #008080000000;">returntot</span> <span style="color: #0000000000FF;">1+=</span> <span style="color: #7060A8;">power</span><span style="color: #0000FF;">-(</span><span style="color: #7060A8000000;">mpfr_get_dx</span><span style="color: #0000FF;">(,</span><span style="color: #000000;">zm</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;">ak</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>
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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;">" 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;">9392</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>
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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 0.80125195690120088012519569012007
2 0.57240670447087985724067044708797
4 0.26146412994911062614641299491101
8 0.04601170568923140460117056892316
16 0.00113398428978530011339842897863
32 5.233466447984724e233466446874501e-7
 
For the airport data, diff total is 4.512820512820513,
degrees of freedom is 3,
ch-squared is 0.088753925984435,
p value is 0.788850426319306788850426319307
</pre>
[[File:Phixplotchisquared.png|thumb|center]]
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