CodeCogs

Calculates the negative binomial distribution PDF.

Interface

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

using namespace Statistics::Distributions::Discrete::Negativebinomial;

double PDF(int x, int r, double p)

The negative binomial distribution, also known as the Pascal distribution or Polya distribution, gives the probability of r -1 successes and x failures in x+r - 1 trials, and success on the (x+r) trial. The probability density is given by

$P_{r,p} = \left ( \begin{array}{c}x+r-1\\r-1 \end{array} \right ) p^r (1-p)^x$

(1)

where:

$\left ( \begin{array}{c}x\\y \end{array} \right ) = \frac{x!}{(y! (x-y)!}$

(2)

Example 1

#include <iostream>
#include <codecogs/stats/dists/discrete/negativebinomial/pdf.h>
using namespace Stats::Dists::Discrete::NegativeBinomial;

int main()
{
  std::cout << "\n PDF(10,5,0.25) = " << PDF(10, 5, 0.25);
  return 0;
}

Output:

PDF(10,5,0.25) = 0.0550487

Parameters

the number of failures

the threshold number of successes

the probability of success in each trial

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Result –