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# CDF inv

Inverse of the Poisson distribution CDF
Controller: CodeCogs
Contents

C++
Excel

## CDF Inv

 doubleCDF_inv( int k double y )
Returns the Poisson variable x such that the integral from 0 to x of the Poisson density is equal to the given probability y.

## Example:

```#include <iostream>
#include <codecogs/stats/dists/discrete/poisson/cdf_inv.h>
#include <codecogs/stats/dists/discrete/poisson/cdf.h>
using namespace Stats::Dists::Discrete::Poisson;
int main()
{
printf( "    x              CDF              INV \n" );
for( double x=0.5; x<16; x+=1.5 )
{
double y = CDF( 5, x );
double z = CDF_inv( 5, y );
printf( "%f \t %f \t %f \n", x, y, z );
}
return getchar();
}```

## Output:

```x              CDF              INV
0.500000         0.999986        0.500000
2.000000         0.983436        2.000000
3.500000         0.857614        3.500000
5.000000         0.615961        5.000000
6.500000         0.369041        6.500000
8.000000         0.191236        8.000000
9.500000         0.088528        9.500000
11.000000        0.037520        11.000000
12.500000        0.014823        12.500000
14.000000        0.005532        14.000000
15.500000        0.001970        15.500000```

### Note

if (k < 0) or (y < 0) or (y >= 1) this function writes to the error stream and returns value -1

### Parameters

 k the number of terms to sum, must not be negative y the probability, must be in range 0..1 (but not equal to 1)

### Returns

the Poisson variable x

### Authors

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

Source code is available when you buy a Commercial licence.

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