CDF inv

Dependents

this module uses 18 subunits Exp_Sub1Ln_Add1beta_regbeta_reg_invLog_GammaGammalogBetaMachine_EpsilonPoly_EvalStirlinglogGammaFraclogGammaSumasympt_expnXsub_Ln_Add1errorFnCerrorFnC_expExpx2errorFn

Interface

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.

Example:

#include <stdio.h>
#include <codecogs/stats/dists/discrete/binomial/cdf_inv.h>
#include <codecogs/stats/dists/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

k	the maximum number of successes, must be >= 0
n	the total number of trials, must be >= k
y	the probability of at most k successes in n 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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