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