poisson_dist.cpp

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#include <cmath>
#include <iostream>
 
double poisson_rate(double events, double timeframe) {
    return events / timeframe;
}
 
double poisson_expected(double rate, double time) { return rate * time; }
 
double fact(double x) {
    double x_fact = x;
    for (int i = x - 1; i > 0; i--) {
        x_fact *= i;
    }
 
    if (x_fact <= 0) {
        x_fact = 1;
    }
    return x_fact;
}
 
double poisson_x_successes(double expected, double x) {
    return (std::pow(expected, x) * std::exp(-expected)) / fact(x);
}
 
double poisson_range_successes(double expected, double lower, double upper) {
    double probability = 0;
    for (int i = lower; i <= upper; i++) {
        probability += poisson_x_successes(expected, i);
    }
    return probability;
}
 
int main() {
    double rate, expected;
    rate = poisson_rate(3, 1);
    std::cout << "Poisson rate : " << rate << std::endl;
 
    expected = poisson_expected(rate, 2);
    std::cout << "Poisson expected : " << expected << std::endl;
 
    std::cout << "Poisson 0 successes : " << poisson_x_successes(expected, 0)
              << std::endl;
    std::cout << "Poisson 0-8 successes : "
              << poisson_range_successes(expected, 0, 8) << std::endl;
 
    return 0;
}