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CDF inv

The negative binomial distribution inverse CDF
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CDF Inv

 doubleCDF_inv( int k int n double p bool upper = false )
Functional inverse of negative binomial distribution CDF. Finds the argument p such that CDF(k,n,p) is equal to y.

Example:

#include <stdio.h>

using namespace Stats::Dists::Discrete::NegativeBinomial;
int main()
{
printf( "    x              CDF              INV \n" );
for( double x=0; x<1; x+=0.1 )
{
double y = CDF( 5, 10, x );
double z = CDF_inv( 5, 10, y );
printf( "%f \t %f \t %f \n", x, y, z );
}
return getchar();
}

Output:

x              CDF              INV
0.000000         0.000000        0.000000
0.100000         0.000000        0.100000
0.200000         0.000113        0.200000
0.300000         0.003653        0.300000
0.400000         0.033833        0.400000
0.500000         0.150879        0.500000
0.600000         0.403216        0.600000
0.700000         0.721621        0.700000
0.800000         0.938949        0.800000
0.900000         0.997750        0.900000
1.000000         1.000000        1.000000

Accuracy:

Tested at random points (a,b,y) with y between 0 and 1.
a,b domain   # trials      peak         rms
0,100       100000      1.5e-14     8.5e-16

Note

in the example shownn above, the result loses accuracy toward x=1

Parameters

 k the maximum number of failures, must be >= 0 n the number of sucesses p the probability that k or fewer failures precede the nth success in a sequence of Bernoulli trials, must be in range 0..1. upper Default value = false

Returns

the probability of success for each trial

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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