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# CDF

Evaluates the binomial distribution CDF.
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## CDF

 doubleCDF( int k int n double p bool upper = false )
Evaluates the binomial distribution CDF:

## 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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