---

C Library Functions  - nbran (3)

---

NAME

nbran(3f) - [M_datapac:RANDOM] generate negative binomial random numbers

CONTENTS

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE NBRAN(N,P,Npar,Istart,X)

       INTEGER,intent(in)        :: N
       REAL(kind=wp),intent(in)  :: P
       INTEGER,intent(in)        :: Npar
       INTEGER,intent(inout)     :: Istart
       REAL(kind=wp),intent(out) :: X(:)

DESCRIPTION

NBRAN(3f) generates a random sample of size N from the negative binomial distribution with 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 precision trial = P.

INPUT ARGUMENTS

N	The desired integer number of random numbers to be generated.
P	The value of the ’Bernoulli probability’ parameter for the negative binomial distribution. P Should be between 0.0 (exclusively) 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 vector (of dimension at least N) into which the generated random sample of size N from the negative binomial distribution will be placed.

EXAMPLES

Sample program:

   program demo_nbran
   use m_datapac, only : nbran, plott, label, plotxt, sort
   implicit none
   integer,parameter :: n=400
   real              :: p
   integer           :: Npar
   integer           :: Istart
   real              :: x(n)
      call label(’nbran’)
      p=0.4
      Npar=3
      istart=12345
      call nbran(N,P,Npar,Istart,X)
      call plotxt(x,n)
      call sort(x,n,x) ! sort to show distribution
      call plotxt(x,n)
   end program demo_nbran

Results:

The following is a plot of X(I) (vertically) versus I (horizontally) I-----------I-----------I-----------I-----------I

0.2700000E+02 -
	0.2600000E+02 I 0.2500000E+02 I
0.2400000E+02 I
	0.2300000E+02 I 0.2200000E+02 I 0.2100000E+02 -
0.2000000E+02 I
	0.1900000E+02 I
0.1800000E+02 I
	X X X X
0.1700000E+02 I 0.1600000E+02 I
	X X
0.1500000E+02 -
	X X X X X
0.1400000E+02 I
	X X X X X X
0.1300000E+02 I
	X X X X X XX X X XXXX
0.1200000E+02 I
	X X X X X X
0.1100000E+02 I
	XX X X X XX X XXX XXXXX XX XX
0.1000000E+02 I
	X XX XXXX X XXX X XX X X X
0.9000000E+01 -
	XX XXXX XX X XX XX X X X X X XX X
0.8000000E+01 I
	XXXX XX XXX XX XXXXXXX X XX X XXX XXXX X X
0.7000000E+01 I
	XX XXXXXX XXXXX X XXXX X XXX X XXX XXXXX
0.6000000E+01 I
	X XXX X X XXXXXX X X XXX X XXXX X XXXXX XXXX X
0.5000000E+01 I
	XXXXXXXXXX XXXXXX XX XX XXX XXXX X XXXXXXXXXXX X
0.4000000E+01 I
	XX X X XXXX XXXX XXXX XX X XXXX XX XX XX X
0.3000000E+01 -
	X XXX XX X XXX XX XXX X XX XX XX X I-----------I-----------I-----------I-----------I 0.1000E+01   0.1008E+03 0.2005E+03 0.3002E+03 0.4000E+03

The following is a plot of X(I) (vertically) versus I (horizontally) I-----------I-----------I-----------I-----------I

0.2700000E+02 -
	0.2600000E+02 I 0.2500000E+02 I
0.2400000E+02 I
	0.2300000E+02 I 0.2200000E+02 I 0.2100000E+02 -
0.2000000E+02 I
	0.1900000E+02 I
0.1800000E+02 I
	XX
0.1700000E+02 I 0.1600000E+02 I 0.1500000E+02 -
	XX
0.1400000E+02 I
	XX
0.1300000E+02 I
	XX
0.1200000E+02 I
	XX
0.1100000E+02 I
	XXXX
0.1000000E+02 I
	XXXX
0.9000000E+01 -
	XXXX
0.8000000E+01 I
	XXXXXXX
0.7000000E+01 I
	XXXXXXX
0.6000000E+01 I
	XXXXXXX
0.5000000E+01 I
	XXXXXXXX
0.4000000E+01 I
	XXXXXX
0.3000000E+01 -
	XXXX I-----------I-----------I-----------I-----------I 0.1000E+01   0.1008E+03 0.2005E+03 0.3002E+03 0.4000E+03

AUTHOR

The original DATAPAC library was written by James Filliben of the Statistical Engineering Division, National Institute of Standards and Technology.

MAINTAINER

John Urban, 2022.05.31

LICENSE

CC0-1.0

REFERENCES

o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, page 95.
o	Johnson and Kotz, Discrete Distributions, 1969, pages 122-142.
o	Feller, an Introduction to Probability Theory and its Applications, Volume 1, Edition 2, 1957, pages 155-157, 210.
o	National Bureau of Standards Applied Mathematics Series 55, 1964, page 929.
o	Kendall and Stuart, the Advanced Theory of Statistics, Volume 1, Edition 2, 1963, pages 130-131.

---

Nemo Release 3.1

nbran (3)

July 22, 2023

Generated by manServer 1.08 from 6c496bb4-8509-4d30-8f4d-b2cfbcc37f26 using man macros.