CDF_inv

Finds the event probability p such that the sum of the terms 0 through k of the Binomial probability density is equal to the given cumulative probability y.

\graph k=1 n=2:10:5 y=0:1

Example:

#include <stdio.h>
#include <codecogs/statistics/distributions/discrete/binomial/cdf_inv.h>
#include <codecogs/statistics/distributions/discrete/binomial/cdf.h>
using namespace Stats::Dists::Discrete::Binomial;
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, true );
    printf( "%f \t %f \t %f \n", x, y, z );
  }
  return getchar();
}

Output:

x              CDF              INV
0.000000         1.000000        0.000000
0.100000         0.999853        0.100000
0.200000         0.993631        0.200000
0.300000         0.952651        0.300000
0.400000         0.833761        0.400000
0.500000         0.623047        0.500000
0.600000         0.366897        0.600000
0.700000         0.150268        0.700000
0.800000         0.032793        0.800000
0.900000         0.001635        0.900000
1.000000         0.000000        1.000000

Accuracy:

Tested at random points (a,b,p).
      p         a,b domain   # trials      peak         rms
0.001 to 1        0,100       100000      2.3e-14     6.4e-16
0.001 to 1        0,10000     100000      6.6e-12     1.2e-13
10^-6 to 0.001    0,100       100000      2.0e-12     1.3e-14
10^-6 to 0.001    0,10000     100000      1.5e-12     3.2e-14

Parameters

Returns