Evaluates the Student’s t distribution function.
Synopsis
#include <imsl.h>
float imsl_f_t_cdf (float t, float df)
The type double function is imsl_d_t_cdf.
Required Arguments
float t
(Input)
Argument for which the Student’s t distribution function is to
be evaluated.
float df
(Input)
Degrees of freedom. Argument df must be greater
than or equal to 1.0.
Return Value
The probability that a Student’s t random variable takes a value less than or equal to the input t.
Description
The function imsl_f_t_cdf evaluates the distribution function of a Student’s t random variable with ν1 = df degrees of freedom. If the square of t is greater than or equal to ν, the relationship of a t to an F random variable (and subsequently, to a beta random variable) is exploited, and percentage points from a beta distribution are used. Otherwise, the method described by Hill (1970) is used. If ν is not an integer, if ν is greater than 19, or if ν is greater than 200, a Cornish-Fisher expansion is used to evaluate the distribution function. If ν is less than 20 and |t| is less than 2.0, a trigonometric series (see Abramowitz and Stegun 1964, equations 26.7.3 and 26.7.4, with some rearrangement) is used. For the remaining cases, a series given by Hill (1970) that converges well for large values of t is used.
Example
This example finds the probability that a t random variable with six degrees of freedom is greater in absolute value than 2.447. The fact that t is symmetric about zero is used.
#include <imsl.h>
main
()
{
float
p;
float t =
2.447;
float df =
6.0;
p =
2.0*imsl_f_t_cdf(-t,df);
printf("Pr(|t(6)| > 2.447) =
%6.4f\n", p);
}
Output
Pr(|t(6)| > 2.447) = 0.0500
Figure 9-2 Plot of Ft(t, 6.0)
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