      SUBROUTINE POIRAN(N,ALAMBA,ISEED,X)
C
C     PURPOSE--THIS SUBROUTINE GENERATES A RANDOM SAMPLE OF SIZE N
C              FROM THE POISSON DISTRIBUTION
C              WITH SINGLE PRECISION
C              TAIL LENGTH PARAMETER = ALAMBA.
C              THE POISSON DISTRIBUTION USED
C              HEREIN HAS MEAN = ALAMBA
C              AND STANDARD DEVIATION = SQRT(ALAMBA).
C              THIS DISTRIBUTION IS DEFINED FOR
C              ALL DISCRETE NON-NEGATIVE INTEGER  X--X = 0, 1, 2, ... .
C              THIS DISTRIBUTION HAS THE PROBABILITY FUNCTION
C              F(X) = EXP(-ALAMBA) * ALAMBA**X / X!.
C              THE POISSON DISTRIBUTION IS THE
C              DISTRIBUTION OF THE NUMBER OF EVENTS
C              IN THE INTERVAL (0,ALAMBA) WHEN
C              THE WAITING TIME BETWEEN EVENTS
C              IS EXPONENTIALLY DISTRIBUTED
C              WITH MEAN = 1 AND STANDARD DEVIATION = 1.
C     INPUT  ARGUMENTS--N      = THE DESIRED INTEGER NUMBER
C                                OF RANDOM NUMBERS TO BE
C                                GENERATED.
C                     --ALAMBA = THE SINGLE PRECISION VALUE
C                                OF THE TAIL LENGTH PARAMETER.
C                                ALAMBA SHOULD BE POSITIVE.
C     OUTPUT ARGUMENTS--X      = A SINGLE PRECISION VECTOR
C                                (OF DIMENSION AT LEAST N)
C                                INTO WHICH THE GENERATED
C                                RANDOM SAMPLE WILL BE PLACED.
C     OUTPUT--A RANDOM SAMPLE OF SIZE N
C             FROM THE POISSON DISTRIBUTION
C             WITH TAIL LENGTH PARAMETER = ALAMBA.
C     PRINTING--NONE UNLESS AN INPUT ARGUMENT ERROR CONDITION EXISTS.
C     RESTRICTIONS--THERE IS NO RESTRICTION ON THE MAXIMUM VALUE
C                   OF N FOR THIS SUBROUTINE.
C                 --ALAMBA SHOULD BE POSITIVE.
C     OTHER DATAPAC   SUBROUTINES NEEDED--UNIRAN.
C     FORTRAN LIBRARY SUBROUTINES NEEDED--ALOG.
C     MODE OF INTERNAL OPERATIONS--SINGLE PRECISION.
C     LANGUAGE--ANSI FORTRAN (1977)
C     COMMENT--THE SINGLE PRECISION TAIL LENGTH
C              PARAMETER ALAMBA IS     NOT     RESTRICTED
C              TO ONLY INTEGER VALUES.
C              ALAMBA CAN BE SET TO ANY POSITIVE REAL
C              VALUE--INTEGER OR NON-INTEGER.
C     COMMENT--NOTE THAT EVEN THOUGH THE OUTPUT
C              FROM THIS DISCRETE RANDOM NUMBER
C              GENERATOR MUST NECESSARILY BE A
C              SEQUENCE OF ***INTEGER*** VALUES,
C              THE OUTPUT VECTOR X IS SINGLE
C              PRECISION IN MODE.
C              X HAS BEEN SPECIFIED AS SINGLE
C              PRECISION SO AS TO CONFORM WITH THE DATAPAC
C              CONVENTION THAT ALL OUTPUT VECTORS FROM ALL
C              DATAPAC SUBROUTINES ARE SINGLE PRECISION.
C              THIS CONVENTION IS BASED ON THE BELIEF THAT
C              1) A MIXTURE OF MODES (FLOATING POINT
C              VERSUS INTEGER) IS INCONSISTENT AND
C              AN UNNECESSARY COMPLICATION
C              IN A DATA ANALYSIS; AND
C              2) FLOATING POINT MACHINE ARITHMETIC
C              (AS OPPOSED TO INTEGER ARITHMETIC)
C              IS THE MORE NATURAL MODE FOR DOING
C              DATA ANALYSIS.
C     REFERENCES--COX AND MILLER, THE THEORY OF STOCHASTIC
C                 PROCESSES, 1965, PAGE 7.
C               --TOCHER, THE ART OF SIMULATION,
C                 1963, PAGES 36-37.
C               --JOHNSON AND KOTZ, DISCRETE
C                 DISTRIBUTIONS, 1969, PAGES 87-121.
C               --HASTINGS AND PEACOCK, STATISTICAL
C                 DISTRIBUTIONS--A HANDBOOK FOR
C                 STUDENTS AND PRACTITIONERS, 1975,
C                 PAGES 108-113.
C               --FELLER, AN INTRODUCTION TO PROBABILITY
C                 THEORY AND ITS APPLICATIONS, VOLUME 1,
C                 EDITION 2, 1957, PAGES 146-154.
C               --NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS
C                 SERIES 55, 1964, PAGE 929.
C     WRITTEN BY--JAMES J. FILLIBEN
C                 STATISTICAL ENGINEERING DIVISION
C                 CENTER FOR APPLIED MATHEMATICS
C                 NATIONAL BUREAU OF STANDARDS
C                 WASHINGTON, D. C. 20234
C                 PHONE--301-921-3651
C     NOTE--DATAPLOT IS A REGISTERED TRADEMARK
C           OF THE NATIONAL BUREAU OF STANDARDS.
C           THIS SUBROUTINE MAY NOT BE COPIED, EXTRACTED,
C           MODIFIED, OR OTHERWISE USED IN A CONTEXT
C           OUTSIDE OF THE DATAPLOT LANGUAGE/SYSTEM.
C     LANGUAGE--ANSI FORTRAN (1966)
C               EXCEPTION--HOLLERITH STRINGS IN FORMAT STATEMENTS
C                          DENOTED BY QUOTES RATHER THAN NH.
C     VERSION NUMBER--82.6
C     ORIGINAL VERSION--NOVEMBER  1975.
C     UPDATED         --DECEMBER  1981.
C     UPDATED         --MAY       1982.
C
C-----CHARACTER STATEMENTS FOR NON-COMMON VARIABLES-------------------
C
C---------------------------------------------------------------------
C
      DIMENSION X(*)
C
C---------------------------------------------------------------------
C
CCCCC CHARACTER*4 IFEEDB
CCCCC CHARACTER*4 IPRINT
C
CCCCC COMMON /MACH/IRD,IPR,CPUMIN,CPUMAX,NUMBPC,NUMCPW,NUMBPW
CCCCC COMMON /PRINT/IFEEDB,IPRINT
C
      IPR=6
C
C-----START POINT-----------------------------------------------------
C
C     CHECK THE INPUT ARGUMENTS FOR ERRORS
C
      IF(N.LT.1)GOTO50
      IF(ALAMBA.LE.0.0)GOTO55
      GOTO90
   50 WRITE(IPR, 5)
      WRITE(IPR,47)N
      RETURN
   55 WRITE(IPR,15)
      WRITE(IPR,46)ALAMBA
      RETURN
   90 CONTINUE
    5 FORMAT(1H , 91H***** FATAL ERROR--THE FIRST  INPUT ARGUMENT TO THE
     1 POIRAN SUBROUTINE IS NON-POSITIVE *****)
   15 FORMAT(1H , 91H***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE
     1 POIRAN SUBROUTINE IS NON-POSITIVE *****)
   46 FORMAT(1H , 35H***** THE VALUE OF THE ARGUMENT IS ,E15.8,6H *****)
   47 FORMAT(1H , 35H***** THE VALUE OF THE ARGUMENT IS ,I8   ,6H *****)
C
C     GENERATE N POISSON RANDOM NUMBERS
C     USING THE FACT THAT THE DISTRIBUTION
C     OF EXPONENTIAL WAITING TIMES IS POISSON.
C
      DO100I=1,N
      SUM=0.0
      J=1
  150 CALL UNIRAN(1,ISEED,U)
      E=-ALOG(1.0-U)
      SUM=SUM+E
      IF(SUM.GT.ALAMBA)GOTO250
      J=J+1
      GOTO150
  250 X(I)=J-1
  100 CONTINUE
C
      RETURN
      END
