CHSRAN Subroutine

public subroutine CHSRAN(N, Nu, Iseed, X)

NAME

chsran(3f) - [M_datapac:RANDOM] generate chi-square random numbers

SYNOPSIS

   SUBROUTINE CHSRAN(N,Nu,Iseed,X)

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

DESCRIPTION

CHSRAN(3f) generates a random sample of size n from the chi-squared
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 chi-squared
       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
       sequence walk.

OUTPUT ARGUMENTS

–X A vector (of dimension at least N) into which the generated random sample of size N from the chi-squared distribution will be placed.

EXAMPLES

Sample program:

program demo_chsran
use m_datapac, only : chsran, plott, label, plotxt, sort
implicit none
integer,parameter :: n=4000
integer           :: iseed
integer           :: Nu
real              :: x(n)
   call label('chsran')
   Nu=8
   iseed=12345
   call chsran(N,Nu,Iseed,X)
   call plotxt(x,n)
   call sort(x,n,x) ! sort to show distribution
   call plotxt(x,n)
end program demo_chsran

Results:

 THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                   I-----------I-----------I-----------I-----------I
  0.3098298E+02 -                                                  X
  0.2972390E+02 I
  0.2846483E+02 I
  0.2720575E+02 I         X
  0.2594668E+02 I        X                 X
  0.2468760E+02 I
  0.2342853E+02 -      X  X                                     X
  0.2216945E+02 I   X             X  X          X              X  X
  0.2091037E+02 I     X     X  X   X X     XX   X  X  XX       X
  0.1965130E+02 I    XXX XX X  XX  X XXX  X     XX  X   XX    X
  0.1839222E+02 I    XXX  X X  XXXXXXX XXX XXX XXXX XX X   X   X XXX
  0.1713315E+02 I   XX X XXX XX XXXX XXXXX XXXX XXX  XXXXX  XXX XX
  0.1587407E+02 -  XXXXXX XXXXXX XX XXXX XX XXX  X  XX XXXX XX XXXX
  0.1461500E+02 I   XXXXXXXXX XX XXXXXXXXX XX XXX XXXXXX X XXXXXXXX
  0.1335592E+02 I  X XXXXX XXXXXXX XXX XXX XX XXXXXXX XXXXXXXX XXXX
  0.1209685E+02 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.1083777E+02 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.9578695E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.8319620E+01 -   XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.7060543E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.5801468E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.4542393E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.3283318E+01 I  XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.2024242E+01 I  XXX XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
  0.7651675E+00 -   X X X        X      XX  X   XXX X XX    X
                   I-----------I-----------I-----------I-----------I
            0.1000E+01  0.1001E+04  0.2000E+04  0.3000E+04  0.4000E+04

 THE FOLLOWING IS A PLOT OF X(I) (VERTICALLY) VERSUS I (HORIZONTALLY
                   I-----------I-----------I-----------I-----------I
  0.3098298E+02 -                                                  X
  0.2972390E+02 I
  0.2846483E+02 I
  0.2720575E+02 I                                                  X
  0.2594668E+02 I                                                  X
  0.2468760E+02 I
  0.2342853E+02 -                                                  X
  0.2216945E+02 I                                                  X
  0.2091037E+02 I                                                  X
  0.1965130E+02 I                                                 XX
  0.1839222E+02 I                                                 X
  0.1713315E+02 I                                                XX
  0.1587407E+02 -                                               XX
  0.1461500E+02 I                                              XX
  0.1335592E+02 I                                            XXX
  0.1209685E+02 I                                         XXXX
  0.1083777E+02 I                                      XXXX
  0.9578695E+01 I                                 XXXXXX
  0.8319620E+01 -                            XXXXXX
  0.7060543E+01 I                     XXXXXXXX
  0.5801468E+01 I               XXXXXXX
  0.4542393E+01 I         XXXXXXX
  0.3283318E+01 I    XXXXXX
  0.2024242E+01 I  XXX
  0.7651675E+00 -  X
                   I-----------I-----------I-----------I-----------I
            0.1000E+01  0.1001E+04  0.2000E+04  0.3000E+04  0.4000E+04

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

  • Tocher, The Art of Simulation, 1963, pages 34-35.
  • Mood and Grable, Introduction to the Theory of Statistics, 1963, pages 226-227.
  • Johnson and Kotz, Continuous Univariate Distributions–1, 1970, page 171.
  • Hastings and Peacock, Statistical Distributions–A Handbook for Students and Practitioners, 1975, page 48.

Arguments

Type IntentOptional Attributes Name
integer, intent(in) :: N
integer, intent(in) :: Nu
integer, intent(inout) :: Iseed
real(kind=wp), intent(out) :: X(:)

Source Code

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

REAL(kind=wp) :: arg1 , arg2 , sum , y , z
INTEGER i , j
!
DIMENSION y(2) , z(2)
!
!---------------------------------------------------------------------
!
!     CHECK THE INPUT ARGUMENTS FOR ERRORS
!
      IF ( N<1 ) THEN
         WRITE (G_IO,99001)
         99001 FORMAT (' ***** FATAL ERROR--The first input argument to CHSRAN(3f) is non-positive *****')
         WRITE (G_IO,99003) N
         RETURN
      ELSEIF ( Nu<=0 ) THEN
         WRITE (G_IO,99002)
         99002 FORMAT (' ***** FATAL ERROR--The second input argument to CHSRAN(3f) is non-positive *****')
         WRITE (G_IO,99003) Nu
         RETURN
      ELSE
!
!     GENERATE N CHI-SQUARED RANDOM NUMBERS USING THE DEFINITION THAT
!     A CHI-SQUARED VARIATE WITH NU DEGREES OF FREEDOM EQUALS THE SUM OF NU SQUARED NORMAL VARIATES.
!     FIRST GENERATE 2 UNIFORM (0,1) RANDOM NUMBERS, THEN GENERATE 2 NORMAL RANDOM NUMBERS,
!     THEN FORM THE SUM OF SQUARED NORMAL RANDOM NUMBERS.
!
         DO i = 1 , N
            sum = 0.0_wp
            DO j = 1 , Nu , 2
               CALL UNIRAN(2,Iseed,y)
               arg1 = -2.0_wp*LOG(y(1))
               arg2 = 2.0_wp*G_pi*y(2)
               z(1) = (SQRT(arg1))*(COS(arg2))
               z(2) = (SQRT(arg1))*(SIN(arg2))
               sum = sum + z(1)*z(1)
               IF ( j/=Nu ) sum = sum + z(2)*z(2)
            ENDDO
            X(i) = sum
         ENDDO
      ENDIF
99003 FORMAT (' ','***** The value of the argument is ',I0,' *****')
!
END SUBROUTINE CHSRAN