poisson_dist.cpp File Reference

Poisson statistics More...

#include <cmath>
#include <iostream>

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Functions
double	poisson_rate (double events, double timeframe)
double	poisson_expected (double rate, double time)
double	fact (double x)
double	poisson_x_successes (double expected, double x)
double	poisson_range_successes (double expected, double lower, double upper)
int	main ()

Detailed Description

Poisson statistics

The Poisson distribution counts how many events occur over a set time interval.

Function Documentation

fact()

double fact

(

double

x

)

Compute factorial of a given number

                      {
    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;
}

main()

int main

(

void

)

main function

           {
    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;
}

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poisson_expected()

double poisson_expected	(	double	rate,
		double	time
	)

calculate the expected value over a time e.g rate of 2.5 over 10 mins = 2.5 x 10 = 25

{ return rate * time; }

poisson_range_successes()

double poisson_range_successes	(	double	expected,
		double	lower,
		double	upper
	)

probability of a success in range for Poisson dist (inclusive, inclusive)

\[P = \sum_i p(\mu,i)\]

                                                                            {
    double probability = 0;
    for (int i = lower; i <= upper; i++) {
        probability += poisson_x_successes(expected, i);
    }
    return probability;
}

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poisson_rate()

double poisson_rate	(	double	events,
		double	timeframe
	)

poisson rate:
calculate the events per unit time
e.g 5 dollars every 2 mins = 5 / 2 = 2.5

                                                     {
    return events / timeframe;
}

poisson_x_successes()

double poisson_x_successes	(	double	expected,
		double	x
	)

Find the probability of x successes in a Poisson dist.

\[p(\mu,x) = \frac{\mu^x e^{-\mu}}{x!}\]

                                                      {
    return (std::pow(expected, x) * std::exp(-expected)) / fact(x);
}

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