CDF_inv

Finds the Chi-square argument x such that the integral from x to infinity of the Chi-square PDF (in other words the upper CDF) is equal to the given cumulative probability y. This is accomplished using the inverse gamma integral function and the relation: x/2 = gammaUpper_reg_inv( r/2, y );

Example:

#include <stdio.h>
#include <codecogs/stats/dists/continuous/chisquared/cdf_inv.h>
#include <codecogs/stats/dists/continuous/chisquared/cdf.h>
using namespace Stats::Dists::Continuous::ChiSquared;
int main()
{
  printf( "    x              CDF              INV \n" );
  for( double x=1; x<10; x+=0.5 )
  {
    double y = CDF( 5, x, true );
    double z = CDF_inv( 5, y );
    printf( "%f \t %f \t %f \n", x, y, z );
  }
  return getchar();
}

Output:

x              CDF              INV
1.000000         0.962566        1.000000
1.500000         0.913070        1.500000
2.000000         0.849145        2.000000
2.500000         0.776495        2.500000
3.000000         0.699986        3.000000
3.500000         0.623388        3.500000
4.000000         0.549416        4.000000
4.500000         0.479883        4.500000
5.000000         0.415880        5.000000
5.500000         0.357946        5.500000
6.000000         0.306219        6.000000
6.500000         0.260558        6.500000
7.000000         0.220640        7.000000
7.500000         0.186030        7.500000
8.000000         0.156236        8.000000
8.500000         0.130748        8.500000
9.000000         0.109064        9.000000
9.500000         0.090707        9.500000

Parameters

if r<1, y<0 or y>1 this function writes to the error stream and returns -1