C Library Functions  - nbppf (3)

NAME
nbppf(3f) - [M_datapac:PERCENT_POINT] compute the negative binomial percent point function

CONTENTS

Synopsis
Description
Options
Examples
Author
Maintainer
License
References

SYNOPSIS
SUBROUTINE NBPPF(P,Ppar,N,Ppf)

DESCRIPTION
nbppf(3f) computes the percent point function value at the precision precision value p for the negative binomial distribution with precision precision ’bernoulli probability’ parameter = ppar, and integer

the negative binomial distribution used herein has mean = n*(1-ppar)/ppar and standard deviation = sqrt(n*(1-ppar)/(ppar*ppar))). this distribution is defined for all non-negative integer x--x = 0, 1, 2, ... .

this distribution has the probability function 

       f(x) = c(n+x-1,n) * ppar**n * (1-ppar)**x.
where c(n+x-1,n) is the combinatorial function equaling the number of combinations of n+x-1 items taken n at a time.

the negative binomial distribution is the distribution of the number of failures before obtaining n successes in an indefinite sequence of bernoulli (0,1) trials where the probability of success in a precision trial = ppar.

note that the percent point function of a distribution is identically the same as the inverse cumulative distribution function of the distribution.

OPTIONS
X description of parameter
Y description of parameter

EXAMPLES
Sample program: 

   program demo_nbppf
   use M_datapac, only : nbppf
   implicit none
   ! call nbppf(x,y)
   end program demo_nbppf
Results:

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 JOHNSON AND KOTZ, DISCRETE DISTRIBUTIONS, 1969, pages 122-142, ESPECIALLY page 127, FORMULA 22.
o HASTINGS AND PEACOCK, STATISTICAL DISTRIBUTIONS--A HANDBOOK FOR STUDENTS AND PRACTITIONERS, 1975, pages 92-95.
o NATIONAL BUREAU OF STANDARDS APPLIED MATHEMATICS SERIES 55, 1964, page 929.
o FELLER, AN INTRODUCTION TO PROBABILITY THEORY AND ITS APPLICATIONS, VOLUME 1, EDITION 2, 1957, pages 155-157, 210.
o KENDALL AND STUART, THE ADVANCED THEORY OF STATISTICS, VOLUME 1, EDITION 2, 1963, pages 130-131.
o WILLIAMSON AND BRETHERTON, TABLES OF THE NEGATIVE BINOMIAL PROBABILITY DISTRIBUTION, 1963.
o OWEN, HANDBOOK OF STATISTICAL TABLES, 1962, page 304.

Nemo Release 3.1 nbppf (3) February 23, 2025
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