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>
int 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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