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Evaluates the F distribution CDF

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Interface

#include <codecogs/statistics/distributions/continuous/f/cdf.h>

using namespace Statistics::Distributions::Continuous::F;

double CDF( int m, int n, double x, bool upper = false)

This function evaluates the F distribution CDF.

Accuracy:

Tested at random points (m,n,x).

domain x  domain m,n  # trials     peak         rms
  0,1      1,100       100000     3.7e-14     5.9e-16
  1,5      1,100       100000     8.0e-15     1.6e-15
  0,1      1,10000     100000     1.8e-11     3.5e-13
  1,5      1,10000     100000     2.0e-11     3.0e-12

Example:

#include <stdio.h>
#include <codecogs/stats/dists/continuous/f/cdf.h>
using namespace Stats::Dists::Continuous::F;
int main()
{
  int m[10] = { 7, 7, 6, 7, 6, 7, 9, 9, 1, 11 };
  int n[10] = { 5, 8, 3, 7, 5, 5, 4, 5, 11, 8 };
  double x[10] = {0.3, 0.6, 0.9, 0.6, 0.1, 0.4, 0.8, 0.3, 1.0, 0.2 };
  for( int i=0; i<10; i++ )
    printf(  "CDF( %i, %i, %1.1f, true ) = %f \n",
      m[i], n[i], x[i], CDF( m[i], n[i], x[i] )  );
  return getchar();
}

Output:

CDF( 7, 5, 0.3, true ) = 0.926089
CDF( 7, 8, 0.6, true ) = 0.742601
CDF( 6, 3, 0.9, true ) = 0.584629
CDF( 7, 7, 0.6, true ) = 0.741755
CDF( 6, 5, 0.1, true ) = 0.992880
CDF( 7, 5, 0.4, true ) = 0.867994
CDF( 9, 4, 0.8, true ) = 0.642990
CDF( 9, 5, 0.3, true ) = 0.944103
CDF( 1, 11, 1.0, true ) = 0.338801
CDF( 11, 8, 0.2, true ) = 0.991790

Parameters

1st number of degrees of freedom, must be strictly positive

2nd number of degrees of freedom, must be strictly positive

the value at which to evaluate the function, must be positive

upper

Default value = false

Interactive Calculator

upper

Result –