complementary_t_cdf
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.
Argument for which Pr(x > t) is to be evaluated.
float df (Input)
Degrees of freedom. Argument df must be greater than or equal to 1.0.
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 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 t2 ≥ ν, the following identity relating the complementary Student’s t cumulative distribution function, denoted by , to the incomplete beta ratio function is used:
where
and
If t2 < ν, the solution space is partitioned into four algorithms as follows: If ν ≥ 64 and t2/ν ≤ 0.1, a Cornish-Fisher expansion is used to evaluate the distribution function. If ν < 64 and an integer and |t| < 2.0, a trigonometric series is used (see Abramowitz and Stegun 1964, Equations 26.7.3 and 26.7.4 with some rearrangement). If ν < 64 and an integer and |t| ≥ 2.0, a series given by Hill (1970) that converges well for large values of t is used. For the remaining t2 < ν cases, is calculated using the identity:
where
This function provides higher right tail accuracy for the Student's t distribution.
Figure 20, 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 t = 2.447, df = 6.0, p;
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
