CDF

Evaluates the binomial distribution CDF.

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Interface
CDF
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Dependents

Interface

C++

CDF

doubleCDF(	int	`k`
	int	`n`
	double	`p`
	bool	`upper` `= false`	)

Evaluates the binomial distribution CDF:

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

(2)

There is an error with your graph parameters for CDF with options k=1 n=2:10:5 p=0:1

Error Message:Function CDF failed. Ensure that: Invalid C++

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

k	the maximum number of successes
n	the total number of trials, must be >= k
p	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

Authors

Stephen L. Moshier (June 2000)
Updated by Vince Cole (April 2005)

Source Code

Source code is available when you agree to a GP Licence or buy a Commercial Licence.

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