NBRAN
      SUBROUTINE NBRAN(N,P,NPAR,ISTART,X)
  
PURPOSE--This subroutine generates a random sample of size N
         from the negative binomial distribution with single
         precision 'bernoulli probability' parameter = P, and
         integer 'number of successes in bernoulli trials'
         parameter = NPAR.  The negative binomial distribution
         used herein has MEAN = NPAR*(1-P)/P and STANDARD
         DEVIATION = SQRT(NPAR*(1-P)/(P*P))).  This distribution
         is defined for all non-negative integer X--X = 0, 1, 2,
         ...  .  This distribution has the probability function
         F(X) = C(NPAR+X-1,NPAR) * P**NPAR * (1-P)**X.  Where
         C(NPAR+X-1,NPAR) is the combinatorial function equaling
         the number of combinations of NPAR+X-1 items taken NPAR
         at a time.  The negative binomial distribution is the
         distribution of the number of failures before obtaining
         npar successes in an indefinite sequence of bernoulli
         (0,1) trials where the probability of success in a
         single trial = P.
INPUT  ARGUMENTS--N      = The desired integer number of random
                           numbers to be generated.
                --P      = The single precision value of the
                           'bernoulli probability' parameter
                           for the negative binomial
NORPLT                     distbibution.   P should be between
                           0.0 and 1.0 (exclusively).
                --NPAR   = The integer value of the 'number of
                           successes in bernoulli trials'
                           parameter. NPAR should be a positive
                           integer.
                --ISTART = An integer flag code which (if set to
                           0) will start the generator over and
                           hence produce the same random sample
                           over and over again upon successive
                           calls to this subroutine within a
                           run; or (if set to some integer value
                           not equal to 0, like, say, 1) will
                           allow the generator to continue from
                           where it stopped and hence produce
                           different random samples upon
                           successive calls to this subroutine
                           within a run.
OUTPUT ARGUMENTS--X      = A single precision vector (of
                           dimension  least N) into which the g
                           generated random sampleill be placed.
OUTPUT--A random sample of size N from the negative binomial
        distribution with 'bernoulli probability' parameter = P
        and 'number of successes in bernoulli trials'
        parameter = NPAR.
PRINTING--None unless an input argument error condition exists.
RESTRICTIONS--There is no restriction on the maximum value of N
              for this subroutine.
            --P should be between 0.0 and 1.0 (exclusively).
            --NPAR should be a positive integer.
OTHER DATAPAC   SUBROUTINES NEEDED--UNIRAN, BINRAN, GEORAN.
FORTRAN LIBRARY SUBROUTINES NEEDED--None.
MODE OF INTERNAL OPERATIONS--Single precision.
LANGUAGE--ANSI FORTRAN.
COMMENT--Note that even though the output from this discrete
         random number generator must necessarily be a sequence
         of ***integer*** values, the output vector X is single
         precision in mode.  X has been specified as single
         precision so as to conform with the DATAPAC convention
         that all output vectors from all DATAPAC subroutines
         are single precision.  This convention is based on the
         belief that
         1) A mixture of modes (floating point versus integer) is
         inconsistent and an unnecessary complication in a data
         analysis; and
         2) Floating point machine arithmetic (as opposed to
         integer arithmetic) is the more natural mode for doing
         data analysis.
REFERENCES--Hasting and Peacock, Statistical Distributions--A
            Handbook for Students and Practitioners, 1975,
            Page 95.
          --Johnson and Kotz, Discrete Distributions, 1969,
            Pages 122-142.
          --Feller, An Introduction to Probability Theory
            and its Applications, Volume 1, Edition 2, 1957,
            Pages 155-157, 210.
          --National Bureau of Standards Applied Mathematics
            Series 55, 1964, Page 929.
          --Kendall and Stuart, The Advanced Theory of
            Statistics, Volume 1, Edition 2, 1963, Pages 130-131.
WRITTEN BY--James J. Filliben
            Statistical Engineering Laboratory (205.03)
            National Bureau of Standards
            Gaithersburg, MD  20899
            Phone--  301-921-2315
ORIGINAL VERSION--November  1975.