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C Library Functions  - poippf (3)

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NAME

poippf(3f) - [M_datapac:PERCENT_POINT] compute the Poisson percent point function

CONTENTS

Synopsis
Description
Options
Examples
Author
Maintainer
License
References

SYNOPSIS

SUBROUTINE POIPPF(P,Alamba,Ppf)

DESCRIPTION

POIPPF(3f) computes the percent point function value at the precision precision value P for the Poisson distribution with REAL tail length parameter = alamba.

the poisson distribution used herein has mean = alamba and standard deviation = sqrt(alamba). this distribution is defined for all discrete non-negative integer x--x = 0, 1, 2, ... .

this distribution has the probability function

       f(x) = exp(-alamba) * alamba**x / x!.

the poisson distribution is the distribution of the number of events in the interval (0,alamba) when the waiting time between events is exponentially distributed with mean = 1 and standard deviation = 1.

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_poippf
   use M_datapac, only : poippf
   implicit none
   ! call poippf(x,y)
   end program demo_poippf

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 87-121, especially page 102, Formula 36.1.   --Hastings and Peacock, Statistical Distributions--A Handbook for Students and Practitioners, 1975, pages 108-113.
o	National Bureau of Standards Applied Mathematics Series 55, 1964, page 929.   --Feller, An Introduction to Probability Theory and Its Applications, Volume 1, Edition 2, 1957, pages 146-154.
o	Cox and Miller, The Theory of Stochastic Processes, 1965, page 7.
o	General Electric Company, Tables of the Individual and Cumulative Terms of Poisson Distribution, 1962.
o	Owen, Handbook of Statistical Tables, 1962, pages 259-261.

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Nemo Release 3.1

poippf (3)

February 23, 2025

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