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# CDF

Evaluates the negative binomial distribution CDF.
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C++

## CDF

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

 k the maximum number of failures, must be >= 0 n the number of sucesses p the probability of success for each trial, must be in range 0..1 upper Default value = false

### Returns

the probability that more than k failures precede the nth success in a sequence of Bernoulli trials.

### 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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