Evaluates the inverse of the Student's t distribution function.
#include <imsls.h>
float imsls_f_t_inverse_cdf (float p, float df)
The type double function is imsls_d_t_inverse_cdf.
float p
(Input)
Probability for which the inverse of the Student's t
distribution function is to be evaluated. Argument p must be in the open
interval (0.0, 1.0).
float df
(Input)
Degrees of freedom. Argument df must be greater
than or equal to 1.0.
The inverse of the Student's t distribution function evaluated at p. The probability that a Student's t random variable takes a value less than or equal to imsls_f_t_inverse_cdf is p.
Function imsls_f_t_inverse_cdf evaluates the inverse distribution function of a Student's t random variable with ν = df degrees of freedom. If ν equals 1 or 2, the inverse can be obtained in closed form. If ν is between 1 and 2, the relationship of a t to a beta random variable is exploited and the inverse of the beta distribution is used to evaluate the inverse; otherwise, the algorithm of Hill (1970) is used. For small values of ν greater than 2, Hill's algorithm inverts an integrated expansion in 1/(1 + t2/ν) of the t density. For larger values, an asymptotic inverse Cornish-Fisher type expansion about normal deviates is used.
This example finds the 0.05 critical value for a two-sided t test with 6 degrees of freedom.
#include <imsls.h>
int main()
{
float df = 6.0;
float p = 0.975;
float t;
t = imsls_f_t_inverse_cdf(p,df);
printf("The two-sided t(6) 0.05 critical value is %6.3f\n", t);
}
The two-sided t(6) 0.05 critical value is 2.447
IMSLS_OVERFLOW Function imsls_f_t_inverse_cdf is set to machine infinity since overflow would occur upon modifying the inverse value for the F distribution with the result obtained from the inverse beta distribution.
|
Visual Numerics, Inc. PHONE: 713.784.3131 FAX:713.781.9260 |