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# CDF inv

Inverse of the complemented chi-square distribution
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Contents

C++
Excel

## CDF Inv

 doubleCDF_inv( double r double y )
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>

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

between 0 and 1

### Note

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

### Parameters

 r the number of degrees of freedom, must be at least 1 y the cumulative probability at which to evaluate the function, must be

### 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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