C Library Functions - binppf (3)

NAME

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

Synopsis
Description
Input Arguments
Output Arguments
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE BINPPF(P,Ppar,N,Ppf)

       REAL(kind=wp) :: P
       REAL(kind=wp) :: Ppar
       REAL(kind=wp) :: Ppf
       INTEGER :: N

DESCRIPTION

BINPPF(3f) computes the percent point function value at the precision precision value P for the binomial distribution with REAL
.Bernoulli probability’ parameter = PPAR, and integer ’number of Bernoulli trials’ parameter = N.
The binomial distribution used herein has mean = N*PPAR and standard deviation = sqrt(N*PPAR*(1-PPAR)).
This distribution is defined for all discrete integer X between 0 (inclusively) and N (inclusively).
This distribution has the probability function
      f(X) = c(N,X) * PPAR**X * (1-PPAR)**(N-X).
where c(N,X) is the combinatorial function equaling the number of combinations of N items taken X at a time.
The binomial distribution is the distribution of the number of successes in N 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.

INPUT ARGUMENTS

P The value (between 0.0 (inclusively) and 1.0 (inclusively)) at which the percent point function is to be evaluated.

PPAR The value of the ’Bernoulli probability’ parameter for the binomial distribution. PPAR should be between 0.0 (exclusively) and 1.0 (exclusively).

N The integer value of the ’number of Bernoulli trials’ parameter. N should be a positive integer.

OUTPUT ARGUMENTS

PPF The percent point function value.

EXAMPLES

Sample program:

program demo_binppf use M_datapac, only : binppf implicit none ! call binppf(x,y) end program demo_binppf

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 50-86, especially page 64, Formula 36.

o Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 36-41.

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 135-142.

o Kendall and Stuart, The Advanced Theory of Statistics, Volume 1, Edition 2, 1963, pages 120-125.

o Mood and Grable, Introduction to the Theory of Statistics, Edition 2, 1963, pages 64-69.

o Owen, Handbook of Statistical Tables, 1962, pages 264-272.

Nemo Release 3.1

binppf (3)

February 23, 2025

Generated by manServer 1.08 from c5cd3bcf-260b-49b4-af6a-97a66bed3d5f using man macros.

P	The value (between 0.0 (inclusively) and 1.0 (inclusively)) at which the percent point function is to be evaluated.
PPAR	The value of the ’Bernoulli probability’ parameter for the binomial distribution. PPAR should be between 0.0 (exclusively) and 1.0 (exclusively).
N	The integer value of the ’number of Bernoulli trials’ parameter. N should be a positive integer.

o	Johnson and Kotz, Discrete Distributions, 1969, pages 50-86, especially page 64, Formula 36.
o	Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 36-41.
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 135-142.
o	Kendall and Stuart, The Advanced Theory of Statistics, Volume 1, Edition 2, 1963, pages 120-125.
o	Mood and Grable, Introduction to the Theory of Statistics, Edition 2, 1963, pages 64-69.
o	Owen, Handbook of Statistical Tables, 1962, pages 264-272.