CDF

This function returns the lower and upper tails of the comulative negative binomial distribution function. The negative binomial distribution, also known as the Pascal distribution or Pólya distribution, gives the probability of r-1 successes and x failures in x+r-1 trials, and success on the (x+r)th trial.

Example:

#include <stdio.h>
#include <codecogs/statistics/distributions/discrete/negativebinomial/cdf.h>
using namespace Stats::Dists::Discrete::NegativeBinomial;
int main()
{
  int k[10] = { 1, 3, 0, 5, 6, 5, 1, 5, 6, 3 };
  int n[10] = { 4, 3, 8, 1, 2, 4, 9, 5, 1, 2 };
  double p[10] = { 0.4, 0.1, 0.7, 0.2, 0.3, 0.6, 0.2, 0.7, 0.3, 0.2 };
  for( int i=0; i<10; i++ )
    printf( "CDF( %i, %i, %1.1f, true ) = %f \n",
      k[i], n[i], p[i], CDF(k[i],n[i],p[i],true) );
  return getchar();
}

Output:

CDF( 1, 4, 0.4, true ) = 0.912960
CDF( 3, 3, 0.1, true ) = 0.984150
CDF( 0, 8, 0.7, true ) = 0.942352
CDF( 5, 1, 0.2, true ) = 0.262144
CDF( 6, 2, 0.3, true ) = 0.255298
CDF( 5, 4, 0.6, true ) = 0.099353
CDF( 1, 9, 0.2, true ) = 0.999996
CDF( 5, 5, 0.7, true ) = 0.047349
CDF( 6, 1, 0.3, true ) = 0.082354
CDF( 3, 2, 0.2, true ) = 0.737280

Accuracy:

Tested at random points (a,b,p) with p between 0 and 1.
a,b domain   # trials      peak         rms
  0,100       100000      1.7e-13     8.8e-15

Parameters

Returns