CodeCogs

Poisson probability density.

Interface

#include <codecogs/statistics/distributions/discrete/poisson/pdf.h>

using namespace Statistics::Distributions::Discrete::Poisson;

double PDF(int n, double lambda )

Calculates the Poisson distribution probability density for a number of events, n, with an expected mean value of $\lambda$ .

$P_v(n) = \frac{(\lambda x)^n e^{-\lambda x}}{n!}$

(1)

where $v= \lambda x$

Example:

#include <iostream>
#include <codecogs/statistics/distributions/discrete/poisson/pdf.h>
using namespace Stats::Dists::Discrete::Poisson;

int main()
{
  std::cout << "\nPoisson distribution probability density of 2 events and 5  mean value is : \n";
  std::cout << "PDF(2,5) = " << PDF(2,5);
  return 0;
}

Output:

Poisson distribution probability density of 2 events and 5  mean value is :
PDF(2,5) = 0.0842243

Parameters

the number of events (or sample size)

lambda

the expected mean value, which must be greater than zero.

Returns

the Poisson distribution probability density. Returns -1 on an error.

Interactive Calculator

lambda

Result –