Evaluates the complement of the Student's t distribution.
Synopsis
#include <imsls.h>
float imsls_f_complementary_t_cdf (float t, float df)
The type double function is imsls_d_complementary_t_cdf.
Required Arguments
float t
(Input)
Argument for which Pr(x > t) is to be
evaluated.
float df
(Input)
Degrees of freedom. Argument df must be greater
than 1.0.
Return Value
The probability that a Student's t random variable takes a value greater than t.
Description
Function imsls_f_complementary_t_cdf evaluates one minus the distribution function of a Student's t random variable with ν = df degrees of freedom. If the square of t is greater than 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, is greater than 19, or 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 is used (see Abramowitz and Stegun 1964, Equations 26.7.3 and 26.7.4 with some rearrangement). For the remaining cases, a series given by Hill (1970) that converges well for large values of t is used.
This function provides higher right tail accuracy for the Student's t distribution.
Figure 11-9 Plot of Ft (t, df)
Example
This example finds the 2-tail probability that a Student's t random variable exceeds 2.447.
#include <imsls.h>
#include <stdio.h>
int main ()
{
float p;
float t = 2.447;
float df = 6.0;
p = 2.0*imsls_f_complementary_t_cdf(t,df);
printf("Pr(|t(%1.0f)| > %4.3f) = %6.4f\n", df, t, p);
}
Output
Pr(|t(6)| > 2.447) = 0.0500
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