Statistics/Chi-squared distribution: Difference between revisions
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=={{header|C++}}==
<syntaxhighlight lang="c++">
#include <iostream>
#include <cmath>
#include <numbers>
#include <iomanip>
#include <array>
// The normalised lower incomplete gamma function.
double gamma_cdf(const double aX, const double aK) {
double result = 0.0;
for ( uint32_t m = 0; m <= 99; ++m ) {
result += pow(aX, m) / tgamma(aK + m + 1);
}
result *= pow(aX, aK) * exp(-aX);
return result;
}
// The cumulative probability function of the Chi-squared distribution.
double cdf(const double aX, const double aK) {
if ( aK > 1'000 && aK < 100 ) {
return 1.0;
}
return ( aX > 0.0 && aK > 0.0 ) ? gamma_cdf(aX / 2, aK / 2) : 0.0;
}
// The probability density function of the Chi-squared distribution.
double pdf(const double aX, const double aK) {
return ( aX > 0.0 ) ? pow(aX, aK / 2 - 1) * exp(-aX / 2) / ( pow(2, aK / 2) * tgamma(aK / 2) ) : 0.0;
}
int main() {
std::cout << " Values of the Chi-squared probability distribution function" << std::endl;
std::cout << " x/k 1 2 3 4 5" << std::endl;
for ( uint32_t x = 0; x <= 10; x++ ) {
std::cout << std::setw(2) << x;
for ( uint32_t k = 1; k <= 5; ++k ) {
std::cout << std::setw(10) << std::fixed << pdf(x, k);
}
std::cout << std::endl;
}
std::cout << "\n Values for the Chi-squared distribution with 3 degrees of freedom" << std::endl;
std::cout << "Chi-squared cumulative pdf p-value" << std::endl;
for ( uint32_t x : { 1, 2, 4, 8, 16, 32 } ) {
const double cumulative_pdf = cdf(x, 3);
std::cout << std::setw(6) << x << std::setw(19) << std::fixed << cumulative_pdf
<< std::setw(14) << ( 1.0 - cumulative_pdf ) << std::endl;
}
const std::array<const std::array<int32_t, 2>, 4> observed =
{ { { 77, 23 }, { 88, 12 }, { 79, 21 }, { 81, 19 } } };
const std::array<const std::array<double, 2>, 4> expected =
{ { { 81.25, 18.75 }, { 81.25, 18.75 }, { 81.25, 18.75 }, { 81.25, 18.75 } } };
double testStatistic = 0.0;
for ( uint64_t i = 0; i < observed.size(); ++i ) {
for ( uint64_t j = 0; j < observed[0].size(); ++j ) {
testStatistic += pow(observed[i][j] - expected[i][j], 2.0) / expected[i][j];
}
}
const uint64_t degreesFreedom = ( observed.size() - 1 ) / ( observed[0].size() - 1 );
std::cout << "\nFor the airport data:" << std::endl;
std::cout << " test statistic : " << std::fixed << testStatistic << std::endl;
std::cout << " degrees of freedom : " << degreesFreedom << std::endl;
std::cout << " Chi-squared : " << std::fixed << pdf(testStatistic, degreesFreedom) << std::endl;
std::cout << " p-value : " << std::fixed << cdf(testStatistic, degreesFreedom) << std::endl;
}
</syntaxhighlight>
{{ 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
1 0.241971 0.303265 0.241971 0.151633 0.080657
2 0.103777 0.183940 0.207554 0.183940 0.138369
3 0.051393 0.111565 0.154180 0.167348 0.154180
4 0.026995 0.067668 0.107982 0.135335 0.143976
5 0.014645 0.041042 0.073225 0.102606 0.122042
6 0.008109 0.024894 0.048652 0.074681 0.097304
7 0.004553 0.015099 0.031873 0.052845 0.074371
8 0.002583 0.009158 0.020667 0.036631 0.055112
9 0.001477 0.005554 0.013296 0.024995 0.039887
10 0.000850 0.003369 0.008500 0.016845 0.028335
Values for the Chi-squared distribution with 3 degrees of freedom
Chi-squared cumulative pdf p-value
1 0.198748 0.801252
2 0.427593 0.572407
4 0.738536 0.261464
8 0.953988 0.046012
16 0.998866 0.001134
32 0.999999 0.000001
For the airport data:
test statistic : 4.512821
degrees of freedom : 3
Chi-squared : 0.088754
p-value : 0.788850
</pre>
=={{header|Java}}==
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