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Evaluates the binomial distribution CDF.

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Interface

#include <codecogs/statistics/distributions/discrete/binomial/cdf.h>

using namespace Statistics::Distributions::Discrete::Binomial;

double CDF( int k, int n, double p, bool upper = false)

Evaluates the binomial distribution CDF:

$P_p(k | n ) = \sum_{i=k+1}^{n} \left ( \begin{array}{c}n\\k\end{array} \right ) p^i (1-p)^{n-i}$

(1)

\graph k=1 n=2:10:5 p=0:1

Example:

#include <stdio.h>
#include <codecogs/statistics/distributions/discrete/binomial/cdf.h>
int main()
{
  int k[10] = { 1, 2, 9, 9, 1, 0, 2, 1, 6, 8 };
  int n[10] = { 2, 4, 10, 14, 5, 2, 10, 1, 10, 18 };
  double p[10] = { 0.5, 0.5, 0.5, 0.6, 0.1, 0.4, 0.9, 0.1, 0.1, 0.4 };
  for( int i=0; i<10; i++ )
  {
    printf( "CDF(%i, %i, %1.1f, true) = %f \n",
      k[i], n[i], p[i], Stats::Dists::Discrete::Binomial::CDF( k[i], n[i], p[i], true ) );
  }
  return getchar();
}

Output:

CDF(1, 2, 0.5, true) = 0.250000
CDF(2, 4, 0.5, true) = 0.312500
CDF(9, 10, 0.5, true) = 0.000977
CDF(9, 14, 0.6, true) = 0.279257
CDF(1, 5, 0.1, true) = 0.081460
CDF(0, 2, 0.4, true) = 0.640000
CDF(2, 10, 0.9, true) = 1.000000
CDF(1, 1, 0.1, true) = 0.000000
CDF(6, 10, 0.1, true) = 0.000009
CDF(8, 18, 0.4, true) = 0.263159

Accuracy:

Tested at random points (a,b,p).
     p       a,b domain   # trials      peak         rms
0.001 to 1     0,100       100000      6.7e-15     8.2e-16
0 to 0.001     0,100       100000      1.5e-13     2.7e-15

Parameters

the maximum number of successes

the total number of trials, must be >= k

the probability of success for each trial, must be in range 0..1

upper

Default value = false

Returns

the value of the upper or lower tail of the binomial CDF with the given arguments

Interactive Calculator

upper

Result –