Evaluates the inverse of the noncentral Student's t distribution function.
Synopsis
#include <imsls.h>
float imsls_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
float
p (Input)
A
Probability for which the inverse of the noncentral Student's t
distribution function is to be evaluated. p must be in the open
interval (0.0, 1.0).
int
df
(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
d = delta,
it determines t0 (= imsls_f_non_central_t_inv_cdf
(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 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 routine 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()
{
float p = .95;
int df = 6;
float delta = 6.0;
float t;
t = imsls_f_non_central_t_inv_cdf(p, df, delta);
printf("The 0.05 noncentral t critical value is %6.4f.\n", t);
}
Output
The 0.05 noncentral t critical value is 11.995.
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