non_central_t_inv_cdf

Evaluates the inverse of the noncentral Student’s tdistribution function.

Synopsis

#include <imsls.h>

floatimsls_f_non_central_t_inv_cdf(float p, int df, float delta)

The type double function is imsls_d_non_central_t_inv_cdf.

Required Arguments

floatp (Input)
A Probability for which the inverse of the noncentral Student’s tdistribution function is to be evaluated.p must be in the open interval (0.0, 1.0).

intdf (Input)
Number of degrees of freedom of the noncentral Student’s t distribution. Argument df must be greater than or equal to 0.0

float delta (Input)
The noncentrality parameter.

Return Value

The probability that a noncentral Student’s t random variable takes a value less than or equal to t is p.

Description

Function imsls_f_non_central_t_inv_cdf evaluates the inverse distribution function of a noncentral t random variable with df degrees of freedom and noncentrality parameter delta; that is, with P = p, v = df, and δ = delta, it determines t0 (= imsls_f_non_central_t_inv_cdf (p, df, delta)), such that

 

where Γ(⋅) is the gamma function. In other words:

 

The probability that the random variable takes a value less than or equal to t0 is P. See imsls_f_non_central_t_cdf for an alternative definition in terms of normal and chi-squared random variables. The function imsls_f_non_central_t_inv_cdf uses bisection and modified regula falsi to invert the distribution function, which is evaluated using function imsls_f_non_central_t_cdf.

Example

In this example, we find the 95-th percentage point for a noncentral t random variable with 6 degrees of freedom and noncentrality parameter 6.

 

#include <imsls.h>

#include <stdio.h>

 

int main()

{

    int df = 6;

    float p = 0.95, delta = 6.0, t;

 

    t = imsls_f_non_central_t_inv_cdf(p, df, delta);

    printf("The %4.2f noncentral t critical value is "

        "%6.4f.\n", 1.0-p, t);

}

Output

 

The 0.05 noncentral t critical value is 11.995.