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 Special Functions/Chapter 4, Gamma and Related Funtions).

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

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