Statistics/Chi-squared distribution: Difference between revisions
Statistics/Chi-squared distribution (view source)
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p-value : 0.788850
</pre>
=={{header|FreeBASIC}}==
{{trans|Wren}}
<syntaxhighlight lang="vb">#define pi 4 * Atn(1)
Function gamma (x As Double) As Double
Dim As Integer k
Dim As Double p(12)
Dim As Double accm = p(1)
If accm = 0 Then
accm = Sqr(2 * pi)
p(1) = accm
Dim As Double k1factrl = 1
For k = 2 To 12
p(k) = Exp(13 - k) * (13 - k)^(k - 1.5) / k1factrl
k1factrl *= -(k - 1)
Next k
End If
For k = 2 To 12
accm += p(k) / (x + k - 1)
Next
accm *= Exp(-(x + 12)) * (x + 12)^(x + .5)
Return accm / x
End Function
Function pdf(x As Double, k As Double) As Double
'probability density function
Return Iif(x <= 0, 0, x^(k / 2 - 1) * Exp(-x / 2) / (2^(k / 2) * gamma(k / 2)))
End Function
Function cpdf(x As Double, k As Double) As Double
'cumulative probability distribution function
Dim As Double t = Exp(-x / 2) * (x / 2)^(k / 2)
Dim As Double s, term
Dim As Uinteger m = 0
Do
term = (x / 2)^m / gamma(k / 2 + m + 1)
s += term
m += 1
Loop Until Abs(term) < 1e-15
Return t * s
End Function
Dim As Integer x, k, i, j
Print " Values of the Chi-squared probability distribution function"
Print " x k = 1 k = 2 k = 3 k = 4 k = 5"
For x = 0 To 10
Print Using "## "; x;
For k = 1 To 5
Print Using "#.############ "; pdf(x, k);
Next
Print
Next
Print !"\n Values for Chi-squared with 3 degrees of freedom"
Print "Chi-squared cum pdf P value"
Dim As Uinteger tt(5) = {1, 2, 4, 8, 16, 32}
For x = 0 To Ubound(tt)
Dim As Double cpdff = cpdf(tt(x), 3)
Print Using " ## #.############ #.############"; tt(x); cpdff; 1-cpdff
Next
Dim As Uinteger airport(3,1) = {{77, 23}, {88, 12}, {79, 21}, {81, 19}}
Dim As Double expected(1) = {81.25, 18.75}
Dim As Double dsum = 0
For i = 0 To Ubound(airport,1)
For j = 0 To Ubound(airport,2)
dsum += (airport(i, j) - expected(j))^2 / expected(j)
Next
Next
Dim As Double dof = Ubound(airport,1) / Ubound(airport,2)
Print Using !"\nFor the airport data, diff total is #.############"; dsum
Print Spc(14); "degrees of freedom is"; dof
Print Spc(21); Using "Chi-squared is #.############"; pdf(dsum, dof)
Print Spc(25); Using "P value is #.############"; cpdf(dsum, dof)
Sleep</syntaxhighlight>
{{out}}
<pre> Values of the Chi-squared probability distribution function
x k = 1 k = 2 k = 3 k = 4 k = 5
0 0.000000000000 0.000000000000 0.000000000000 0.000000000000 0.000000000000
1 0.241970724519 0.303265329856 0.241970724519 0.151632664928 0.080656908173
2 0.103776874355 0.183939720586 0.207553748710 0.183939720586 0.138369165807
3 0.051393443268 0.111565080074 0.154180329804 0.167347620111 0.154180329804
4 0.026995483257 0.067667641618 0.107981933026 0.135335283237 0.143975910702
5 0.014644982562 0.041042499312 0.073224912810 0.102606248280 0.122041521349
6 0.008108695555 0.024893534184 0.048652173330 0.074680602552 0.097304346659
7 0.004553342922 0.015098691711 0.031873400451 0.052845420989 0.074371267720
8 0.002583373169 0.009157819444 0.020666985354 0.036631277777 0.055111960944
9 0.001477282804 0.005554498269 0.013295545236 0.024995242211 0.039886635707
10 0.000850036660 0.003368973500 0.008500366603 0.016844867498 0.028334555342
Values for Chi-squared with 3 degrees of freedom
Chi-squared cum pdf P value
1 0.198748043099 0.801251956901
2 0.427593295529 0.572406704471
4 0.738535870051 0.261464129949
8 0.953988294311 0.046011705689
16 0.998866015710 0.001133984290
32 0.999999476654 0.000000523346
For the airport data, diff total is 4.512820512821
degrees of freedom is 3
Chi-squared is 0.088753925984
P value is 0.788850426319</pre>
=={{header|Java}}==
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System.out.println();
System.out.println(" Values for the Chi-squared distribution with 3 degrees of freedom");
System.out.println("Chi-squared cumulative pdf
for ( int x : List.of( 1, 2, 4, 8, 16, 32 ) ) {
final double cdf = cdf(x, 3);
System.out.println(String.format("%
}
Line 236 ⟶ 345:
private static double gamma(double aX) {
if ( aX < 0.5 ) {
return Math.PI / ( Math.sin(Math.PI * aX
}
Line 259 ⟶ 368:
// The cumulative probability function of the Chi-squared distribution.
private static double cdf(double aX, double aK) {
if ( aX > 1_000 && aK < 100 ) {
return 1.0;
}
return ( aX > 0.0 && aK > 0.0 ) ? gammaCDF(aX / 2, aK / 2) : 0.0;
}
Line 277 ⟶ 389:
{{ out }}
<pre>
Values of the Chi-squared probability distribution function
x/k 1 2 3 4 5
0 0.000000 0.000000 0.000000 0.000000 0.000000
Line 292 ⟶ 404:
Values for the Chi-squared distribution with 3 degrees of freedom
Chi-squared cumulative pdf
1
2
4
8
16
32
For the airport data:
Line 1,002 ⟶ 1,114:
{{libheader|Wren-fmt}}
{{libheader|Wren-plot}}
<syntaxhighlight lang="
import "graphics" for Canvas, Color
import "./math2" for Math
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