Evaluates the inverse of the noncentral chi-squared function.

Synopsis

#include <imsls.h>

float imsls_f_non_central_chi_sq_inv (float p, float df, float delta)

The type double function is imsls_d_non_central_chi_sq_inv.

Required Arguments

float p   (Input)
Probability for which the inverse of the noncentral chi-squared distribution function is to be evaluated. p must be in the open interval (0.0, 1.0).

float df   (Input)
Number of degrees of freedom of the noncentral chi-squared distribution. Argument df must be greater than or equal to 0.5

float delta (Input)
The noncentrality parameter.  delta must be nonnegative, and    delta + df  must be less than or equal to 200,000.

Return Value

The probability that a noncentral chi-squared random variable takes a value less than or equal to imsls_f_non_central_chi_sq_inv is p.

Description

Function imsls_f_non_central_chi_sq_inv evaluates the inverse distribution function of a noncentral chi-squared random variable with
df degrees of freedom and noncentrality parameter delta; that is, with P = p, v = df, and  l = delta, it determines c0 (= imsls_f_non_central_chi_sq_inv (p, df, delta)), such that

where G(×) is the gamma function. The probability that the random variable takes a value less than or equal to c0 is P.

Function imsls_f_non_central_chi_sq_inv uses bisection and modified regula falsi to invert the distribution function, which is evaluated using
routine imsls_f_non_central_chi_sq. See imsls_f_non_central_chi_sq for an alternative definition of the noncentral chi-squared random variable in terms of normal random variables.

Example

In this example, we find the 95-th percentage point for a noncentral chi-squared random variable with 2 degrees of freedom and noncentrality parameter 1.

#include <imsls.h>

#include <stdio.h>

void main()

{

        float p = .95;

        int df = 2;

        float delta = 1.0;

        float chi_squared;

        chi_squared = imsls_f_non_central_chi_sq_inv(p, df, delta);

 printf("The 0.05 noncentral chi-squared critical value is %6.4f.\n",

        chi_squared);

}

Output

The 0.05 noncentral chi-squared critical value is  8.6422.

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