Verify distribution uniformity/Chi-squared test: Difference between revisions

=={{header|C++}}==

<syntaxhighlight lang="c++">

#include <iostream>

#include <vector>

#include <cmath>

#include <iomanip>

void print_vector(const std::vector<int32_t>& list) {

std::cout << "[";

for ( uint64_t i = 0; i < list.size(); ++i ) {

std::cout << list[i] << ", ";

}

std::cout << list.back() << "]" << std::endl;

}

bool is_significant(const double p_value, const double significance_level) {

return p_value > significance_level;

}

// 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 std::isnan(result) ? 1.0 : result;

}

// The cumulative probability function of the Chi-squared distribution.

double cdf(const double aX, const double aK) {

if ( aX > 1'000 && aK < 100 ) {

return 1.0;

}

return ( aX > 0.0 && aK > 0.0 ) ? gamma_cdf(aX / 2, aK / 2) : 0.0;

}

void chi_squared_test(const std::vector<int32_t>& observed) {

double sum = 0.0;

for ( uint64_t i = 0; i < observed.size(); ++i ) {

sum += observed[i];

}

const double expected = sum / observed.size();

const int32_t degree_freedom = observed.size() - 1;

double test_statistic = 0.0;

for ( uint64_t i = 0; i < observed.size(); ++i ) {

test_statistic += pow(observed[i] - expected, 2) / expected;

}

const double p_value = 1.0 - cdf(test_statistic, degree_freedom);

std::cout << "\nUniform distribution test" << std::setprecision(6) << std::endl;

std::cout << " observed values : "; print_vector(observed);

std::cout << " expected value : " << expected << std::endl;

std::cout << " degrees of freedom: " << degree_freedom << std::endl;

std::cout << " test statistic : " << test_statistic << std::endl;

std::cout.setf(std::ios::fixed);

std::cout << " p-value : " << p_value << std::endl;

std::cout.unsetf(std::ios::fixed);

std::cout << " is 5% significant?: " << std::boolalpha << is_significant(p_value, 0.05) << std::endl;

}

int main() {

const std::vector<std::vector<int32_t>> datasets = { { 199809, 200665, 199607, 200270, 199649 },

{ 522573, 244456, 139979, 71531, 21461 } };

for ( std::vector<int32_t> dataset : datasets ) {

chi_squared_test(dataset);

}

}

</syntaxhighlight>

{{ out }}

<pre>

Uniform distribution test

observed values : [199809, 200665, 199607, 200270, 199649, 199649]

expected value : 200000

degrees of freedom: 4

test statistic : 4.14628

p-value : 0.386571

is 5% significant?: true

Uniform distribution test

observed values : [522573, 244456, 139979, 71531, 21461, 21461]

expected value : 200000

degrees of freedom: 4

test statistic : 790063

p-value : 0.000000

is 5% significant?: false

</pre>