---

C Library Functions  - tran (3)

---

NAME

tran(3f) - [M_datapac:RANDOM] a random sample of size n from the Student’s t distribution with integer degrees of freedom parameter NU.

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE TRAN(N,Nu,Iseed,X)

       INTEGER,intent(in)        :: N
       INTEGER,intent(in)        :: Nu
       INTEGER,intent(inout)     :: Iseed
       REAL(kind=wp),intent(out) :: X(:)

DESCRIPTION

This subroutine generates a random sample of size N from the Student’s T distribution with integer degrees of freedom parameter = NU.

INPUT ARGUMENTS

N	The desired integer number of random numbers to be generated.
NU	The integer degrees of freedom (parameter) for the T distribution. NU should be a positive integer variable.

ISEED	An integer seed value. Should be set to a non-negative value to start a new sequence of values. Will be set to -1 on return to indicate the next call should continue the current random

OUTPUT ARGUMENTS

X	A vector (of dimension at least N) into which the generated random sample of size N from the Student’s T distribution will be placed.

EXAMPLES

Sample program:

   program demo_tran
   use m_datapac, only : tran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=400
   real :: x(n)
   integer :: iseed
   integer :: nu
      call label(’tran’)
      nu=3
      iseed=12345
      call tran(N,Nu,Iseed,X)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_tran

Results:

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.1029407E+02 -                                          X
     0.9486016E+01 I
     0.8677961E+01 I
     0.7869905E+01 I
     0.7061851E+01 I                          X
     0.6253795E+01 I                               X
     0.5445739E+01 -
     0.4637684E+01 I
     0.3829628E+01 I          X        X         X      X
     0.3021573E+01 I      X X  X XX       X X     X                 X
     0.2213517E+01 I  X    XX       XX  X    X X      X X   X
     0.1405462E+01 I   X   XXXX XXXXXXXXXXXX XX    XXX  XXX  XXXXXX
     0.5974064E+00 -  XX XXXXXXXXXXXXXXXXXXXXXXXX XXX XXXXXXXXXXXX XXX
    -0.2106485E+00 I   XXXXXXXXXXXXXX XXXXXXXXXXXXXXXXXXXXXX XXXXXXXXXX
    -0.1018704E+01 I  XX XX XX X XXX XX XXXXXXXXXXXX  XX  XXXX XX XXX X
    -0.1826759E+01 I    XXXXXX XX  XX  XX  X   XX  X     X X    XX   XX
    -0.2634815E+01 I     X           XX        X         X   X    XX
    -0.3442871E+01 I          X                   X
    -0.4250926E+01 -                        X          X          X  X
    -0.5058982E+01 I                                X              X
    -0.5867038E+01 I                     X
    -0.6675092E+01 I
    -0.7483148E+01 I
    -0.8291203E+01 I
    -0.9099259E+01 -                          X                      X
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1008E+03  0.2005E+03  0.3002E+03  0.4000E+03

    THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                      I-----------I-----------I-----------I-----------I
     0.1029407E+02 -                                                  X
     0.9486016E+01 I
     0.8677961E+01 I
     0.7869905E+01 I
     0.7061851E+01 I                                                  X
     0.6253795E+01 I                                                  X
     0.5445739E+01 -
     0.4637684E+01 I
     0.3829628E+01 I                                                 XX
     0.3021573E+01 I                                                XX
     0.2213517E+01 I                                              XXX
     0.1405462E+01 I                                         XXXXXX
     0.5974064E+00 -                              XXXXXXXXXXXX
    -0.2106485E+00 I                XXXXXXXXXXXXXXX
    -0.1018704E+01 I        XXXXXXXXX
    -0.1826759E+01 I    XXXXX
    -0.2634815E+01 I   XX
    -0.3442871E+01 I   X
    -0.4250926E+01 -   X
    -0.5058982E+01 I  X
    -0.5867038E+01 I  X
    -0.6675092E+01 I
    -0.7483148E+01 I
    -0.8291203E+01 I
    -0.9099259E+01 -  X
                      I-----------I-----------I-----------I-----------I
               0.1000E+01  0.1008E+03  0.2005E+03  0.3002E+03  0.4000E+03

AUTHOR

The original DATAPAC library was written by James Filliben of the Statistical Engineering Division, National Institute of Standards and Technology.

MAINTAINER

John Urban, 2022.05.31

LICENSE

CC0-1.0

REFERENCES

o	Mood and Grable, Introduction to the Theory of Statistics, 1963, page 233.
o	Johnson and Kotz, Continuous Univariate Distributions--2, 1970, page 94.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 121.

---

Nemo Release 3.1

tran (3)

July 22, 2023

Generated by manServer 1.08 from a32014e0-1e4c-4b03-8753-a9189fb88b36 using man macros.