SUBROUTINE POICDF(X,ALAMBA,CDF) C C PURPOSE--THIS SUBROUTINE COMPUTES THE CUMULATIVE DISTRIBUTION C FUNCTION VALUE AT THE SINGLE PRECISION VALUE X C FOR 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--X = THE SINGLE PRECISION VALUE C AT WHICH THE CUMULATIVE DISTRIBUTION C FUNCTION IS TO BE EVALUATED. C X SHOULD BE NON-NEGATIVE AND C INTEGRAL-VALUED. C --ALAMBA = THE SINGLE PRECISION VALUE C OF THE TAIL LENGTH PARAMETER. C ALAMBA SHOULD BE POSITIVE. C OUTPUT ARGUMENTS--CDF = THE SINGLE PRECISION CUMULATIVE C DISTRIBUTION FUNCTION VALUE. C OUTPUT--THE SINGLE PRECISION CUMULATIVE DISTRIBUTION C FUNCTION VALUE CDF C FOR THE POISSON DISTRIBUTION C WITH TAIL LENGTH PARAMETER = ALAMBA. C PRINTING--NONE UNLESS AN INPUT ARGUMENT ERROR CONDITION EXISTS. C RESTRICTIONS--X SHOULD BE NON-NEGATIVE AND INTEGRAL-VALUED. C --ALAMBA SHOULD BE POSITIVE. C OTHER DATAPAC SUBROUTINES NEEDED--NORCDF. C FORTRAN LIBRARY SUBROUTINES NEEDED--DSQRT, DATAN. C MODE OF INTERNAL OPERATIONS--DOUBLE PRECISION. C LANGUAGE--ANSI FORTRAN. 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 --NOTE THAT EVEN THOUGH THE INPUT C TO THIS CUMULATIVE C DISTRIBUTION FUNCTION SUBROUTINE C FOR THIS DISCRETE DISTRIBUTION C SHOULD (UNDER NORMAL CIRCUMSTANCES) BE A C DISCRETE INTEGER VALUE, C THE INPUT VARIABLE 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 INPUT ****DATA**** C (AS OPPOSED TO SAMPLE SIZE, FOR EXAMPLE) C VARIABLES TO 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--JOHNSON AND KOTZ, DISCRETE C DISTRIBUTIONS, 1969, PAGES 87-121, C ESPECIALLY PAGE 114, FORMULA 93. C --HASTINGS AND PEACOCK, STATISTICAL C DISTRIBUTIONS--A HANDBOOK FOR C STUDENTS AND PRACTITIONERS, 1975, C PAGE 112. C --NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS C SERIES 55, 1964, PAGE 941, FORMULAE 26.4.4 AND 26.4.5, C AND PAGE 929. C --FELLER, AN INTRODUCTION TO PROBABILITY C THEORY AND ITS APPLICATIONS, VOLUME 1, C EDITION 2, 1957, PAGES 146-154. C --COX AND MILLER, THE THEORY OF STOCHASTIC C PROCESSES, 1965, PAGE 7. C --GENERAL ELECTRIC COMPANY, TABLES OF THE C INDIVIDUAL AND CUMULATIVE TERMS OF POISSON C DISTRIBUTION, 1962. C --OWEN, HANDBOOK OF STATISTICAL C TABLES, 1962, PAGES 259-261. C WRITTEN BY--JAMES J. FILLIBEN C STATISTICAL ENGINEERING LABORATORY (205.03) C NATIONAL BUREAU OF STANDARDS C WASHINGTON, D. C. 20234 C PHONE: 301-921-2315 C ORIGINAL VERSION--NOVEMBER 1975. C C--------------------------------------------------------------------- C DOUBLE PRECISION DX,PI,CHI,SUM,TERM,AI,DGCDF DOUBLE PRECISION DSQRT,DEXP DATA PI/3.14159265358979D0/ C IPR=6 C C CHECK THE INPUT ARGUMENTS FOR ERRORS C IF(ALAMBA.LE.0.0)GOTO50 IF(X.LT.0.0)GOTO55 INTX=X+0.0001 FINTX=INTX DEL=X-FINTX IF(DEL.LT.0.0)DEL=-DEL IF(DEL.GT.0.001)GOTO60 GOTO90 50 WRITE(IPR,15) WRITE(IPR,46)ALAMBA CDF=0.0 RETURN 55 WRITE(IPR,4) WRITE(IPR,46)X CDF=0.0 RETURN 60 WRITE(IPR,5) WRITE(IPR,46)X 90 CONTINUE 4 FORMAT(1H , 96H***** NON-FATAL DIAGNOSTIC--THE FIRST INPUT ARGUME 1NT TO THE POICDF SUBROUTINE IS NEGATIVE *****) 5 FORMAT(1H ,100H***** NON-FATAL DIAGNOSTIC--THE FIRST INPUT ARGUME 1NT TO THE POICDF SUBROUTINE IS NON-INTEGRAL *****) 15 FORMAT(1H , 91H***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE 1 POICDF 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-----START POINT----------------------------------------------------- C C EXPRESS THE POISSON CUMULATIVE DISTRIBUTION C FUNCTION IN TERMS OF THE EQUIVALENT CHI-SQUARED C CUMULATIVE DISTRIBUTION FUNCTION, C AND THEN EVALUATE THE LATTER. C DX=ALAMBA DX=2.0D0*DX NU=X+0.0001 NU=2*(1+NU) C 110 CHI=DSQRT(DX) IEVODD=NU-2*(NU/2) IF(IEVODD.EQ.0)GOTO120 C SUM=0.0D0 TERM=1.0/CHI IMIN=1 IMAX=NU-1 GOTO130 C 120 SUM=1.0D0 TERM=1.0D0 IMIN=2 IMAX=NU-2 C 130 IF(IMIN.GT.IMAX)GOTO160 DO100I=IMIN,IMAX,2 AI=I TERM=TERM*(DX/AI) SUM=SUM+TERM 100 CONTINUE C 160 SUM=SUM*DEXP(-DX/2.0D0) IF(IEVODD.EQ.0)GOTO170 SUM=(DSQRT(2.0D0/PI))*SUM SPCHI=CHI CALL NORCDF(SPCHI,GCDF) DGCDF=GCDF SUM=SUM+2.0D0*(1.0D0-DGCDF) 170 CDF=SUM C RETURN END