SUBROUTINE BINRAN(N,P,NPAR,ISEED,X)
C
C     PURPOSE--THIS SUBROUTINE GENERATES A RANDOM SAMPLE OF SIZE N
C              FROM THE BINOMIAL DISTRIBUTION
C              WITH SINGLE PRECISION 'BERNOULLI PROBABILITY'
C              PARAMETER = P,
C              AND INTEGER 'NUMBER OF BERNOULLI TRIALS'
C              PARAMETER = NPAR.
C              THE BINOMIAL DISTRIBUTION USED
C              HEREIN HAS MEAN = NPAR*P
C              AND STANDARD DEVIATION = SQRT(NPAR*P*(1-P)).
C              THIS DISTRIBUTION IS DEFINED FOR ALL
C              DISCRETE INTEGER X BETWEEN 0 (INCLUSIVELY)
C              AND NPAR (INCLUSIVELY).
C              THIS DISTRIBUTION HAS THE PROBABILITY FUNCTION
C              F(X) = C(NPAR,X) * P**X * (1-P)**(NPAR-X).
C              WHERE C(NPAR,X) IS THE COMBINATORIAL FUNCTION
C              EQUALING THE NUMBER OF COMBINATIONS OF NPAR ITEMS
C              TAKEN X AT A TIME.
C              THE BINOMIAL DISTRIBUTION IS THE
C              DISTRIBUTION OF THE NUMBER OF
C              SUCCESSES IN NPAR BERNOULLI (0,1)
C              TRIALS WHERE THE PROBABILITY OF SUCCESS
C              IN A SINGLE TRIAL = P.
C     INPUT  ARGUMENTS--N      = THE DESIRED INTEGER NUMBER
C                                OF RANDOM NUMBERS TO BE
C                                GENERATED.
C                     --P      = THE SINGLE PRECISION VALUE
C                                OF THE 'BERNOULLI PROBABILITY'
C                                PARAMETER FOR THE BINOMIAL
C                                DISTRIBUTION.
C                                P SHOULD BE BETWEEN
C                                0.0 (EXCLUSIVELY) AND
C                                1.0 (EXCLUSIVELY).
C                     --NPAR   = THE INTEGER VALUE
C                                OF THE 'NUMBER OF BERNOULLI TRIALS'
C                                PARAMETER.
C                                NPAR SHOULD BE A POSITIVE INTEGER.
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 BINOMIAL DISTRIBUTION
C             WITH 'BERNOULLI PROBABILITY' PARAMETER = P
C             AND 'NUMBER OF BERNOULLI TRIALS' PARAMETER = NPAR.
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                 --P SHOULD BE BETWEEN 0.0 (EXCLUSIVELY)
C                   AND 1.0 (EXCLUSIVELY).
C                 --NPAR SHOULD BE A POSITIVE INTEGER.
C     OTHER DATAPAC   SUBROUTINES NEEDED--UNIRAN, GEORAN.
C     FORTRAN LIBRARY SUBROUTINES NEEDED--NONE.
C     MODE OF INTERNAL OPERATIONS--SINGLE PRECISION.
C     LANGUAGE--ANSI FORTRAN (1977)
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--JOHNSON AND KOTZ, DISCRETE
C                 DISTRIBUTIONS, 1969, PAGES 50-86.
C               --HASTINGS AND PEACOCK, STATISTICAL
C                 DISTRIBUTIONS--A HANDBOOK FOR
C                 STUDENTS AND PRACTITIONERS, 1975,
C                 PAGE 41.
C               --FELLER, AN INTRODUCTION TO PROBABILITY
C                 THEORY AND ITS APPLICATIONS, VOLUME 1,
C                 EDITION 2, 1957, PAGES 135-142.
C               --NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS
C                 SERIES 55, 1964, PAGE 929.
C               --KENDALL AND STUART, THE ADVANCED THEORY OF
C                 STATISTICS, VOLUME 1, EDITION 2, 1963, PAGES 120-125.
C               --MOOD AND GRABLE, INTRODUCTION TO THE THEORY
C                 OF STATISTICS, EDITION 2, 1963, PAGES 64-69.
C               --TOCHER, THE ART OF SIMULATION,
C                 1963, PAGES 39-40.
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--82/7
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(P.LE.0.0.OR.P.GE.1.0)GOTO55
      IF(NPAR.LT.1)GOTO60
      GOTO90
   50 WRITE(IPR, 5)
      WRITE(IPR,47)N
      RETURN
   55 WRITE(IPR,11)
      WRITE(IPR,46)P
      RETURN
   60 WRITE(IPR,25)
      WRITE(IPR,47)NPAR
      RETURN
   90 CONTINUE
    5 FORMAT(1H , 91H***** FATAL ERROR--THE FIRST  INPUT ARGUMENT TO THE
     1 BINRAN SUBROUTINE IS NON-POSITIVE *****)
   11 FORMAT(1H ,115H***** FATAL ERROR--THE SECOND INPUT ARGUMENT TO THE
     1 BINRAN SUBROUTINE IS OUTSIDE THE ALLOWABLE (0,1) INTERVAL *****)
   25 FORMAT(1H , 91H***** FATAL ERROR--THE THIRD  INPUT ARGUMENT TO THE
     1 BINRAN 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     CHECK ON THE MAGNITUDE OF P,
C     AND BRANCH TO THE FASTER
C     GENERATION METHOD ACCORDINGLY.
C
      IF(P.LT.0.1)GOTO450
C
C     IF P IS MODERATE OR LARGE,
C     GENERATE N BINOMIAL RANDOM NUMBERS
C     USING THE REJECTION METHOD.
C
      DO100I=1,N
      ISUM=0
      DO200J=1,NPAR
      CALL UNIRAN(1,ISEED,U)
      IF(U.LE.P)ISUM=ISUM+1
  200 CONTINUE
      X(I)=ISUM
  100 CONTINUE
      RETURN
C
C     IF P IS SMALL,
C     GENERATE N BINOMIAL NUMBERS
C     USING THE FACT THAT THE
C     WAITING TIME FOR 1 SUCCESS IN
C     BERNOULLI TRIALS HAS A
C     GEOMETRIC DISTRIBUTION.
C
  450 DO500I=1,N
      ISUM=0
      J=1
  550 CALL GEORAN(1,P,ISEED,G)
      IG=G+0.5
      ISUM=ISUM+IG+1
      IF(ISUM.GT.NPAR)GOTO650
      J=J+1
      GOTO550
  650 X(I)=J-1
  500 CONTINUE
      RETURN
C
      END