TPR

This function evaluates the Student's t probability density function

Function Return Value

TPR — Function value, the value of the probability density function. (Output)

Required Arguments

T — Argument for which the Student’s t probability density function is to be evaluated. (Input)

DF — Degrees of freedom. (Input)
DF must be greater than or equal to 1.0.

FORTRAN 90 Interface

Generic: TPR (T, DF)

Specific: The specific interface names are S_TPR and D_TPR

FORTRAN 77 Interface

Single: TPR (T, DF)

Double: The double precision name is DTPR.

Description

The function TPR evaluates the Student’s t probability density function, defined as

 

where ν = DF.

The normalizing factor uses the Beta function, BETA (see the Special Functions book, Chapter 4, Gamma and Related Functions).

Example

In this example, we evaluate the probability function at T = 1.5, DF = 10.0.

 

USE UMACH_INT

USE TPR_INT

IMPLICIT NONE

INTEGER NOUT

REAL T, DF, PR

CALL UMACH(2, NOUT)

T = 1.5

DF = 10.0

PR = TPR(T, DF)

WRITE (NOUT, 99999) T, DF, PR

99999 FORMAT (' TPR(', F4.2, ', ', F6.2, ') = ', F6.4)

END

Output

 

TPR(1.50, 10.00) = 0.1274