RNSTT

Generates pseudorandom numbers from a Student’s t distribution.

Required Arguments

DF — Degrees of freedom. (Input)
DF must be positive.

R — Vector of length NR containing the random Student’s t deviates. (Output)

Optional Arguments

NR — Number of random numbers to generate. (Input)
Default: NR = size (R,1).

FORTRAN 90 Interface

Generic: CALL RNSTT (DF, R [, …])

Specific: The specific interface names are S_RNSTT and D_RNSTT.

FORTRAN 77 Interface

Single: CALL RNSTT (NR, DF, R)

Double: The double precision name is DRNSTT.

Description

Routine RNSTT generates pseudo‑random numbers from a Student’s t distribution with DF degrees of freedom, using a method suggested by Kinderman, Monahan, and Ramage (1977). The method (“TMX” in the reference) involves a representation of the t density as the sum of a triangular density over (–2, 2) and the difference of this and the t density. The mixing probabilities depend on the degrees of freedom of the t distribution. If the triangular density is chosen, the variate is generated as the sum of two uniforms; otherwise, an acceptance/rejection method is used to generate a variate from the difference density.

For degrees of freedom less than 100, RNSTT requires approximately twice the execution time as routine RNNOA which generates pseudorandom normal deviates. The execution time of RNSTT increases very slowly as the degrees of freedom increase. Since for very large degrees of freedom the normal distribution and the t distribution are very similar, the user may find that the difference in the normal and the t does not warrant the additional generation time required to use RNSTT instead of RNNOA.

Comments

The routine RNSET can be used to initialize the seed of the random number generator. The routine RNOPT can be used to select the form of the generator.

Example

In this example, RNSTT is used to generate 5 pseudo‑random t variates with 10 degrees of freedom.

 

USE RNSTT_INT

USE UMACH_INT

USE RNSET_INT

 

IMPLICIT NONE

INTEGER NR

PARAMETER (NR=5)

!

INTEGER ISEED, NOUT

REAL DF, R(NR)

!

CALL UMACH(2, NOUT)

DF = 10.0

ISEED = 123457

CALL RNSET(ISEED)

CALL RNSTT(DF, R)

WRITE(NOUT, 99999) R

99999 FORMAT (' t (10) random deviates: ', 5F8.4)

END

Output

 

t (10) random deviates: 0.6152 1.1528 0.0881 1.3382 -0.9893