nag_poisson_dist (g01bkc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_poisson_dist (g01bkc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_poisson_dist (g01bkc) returns the lower tail, upper tail and point probabilities associated with a Poisson distribution.

2  Specification

#include <nag.h>
#include <nagg01.h>
void  nag_poisson_dist (double rlamda, Integer k, double *plek, double *pgtk, double *peqk, NagError *fail)

3  Description

Let X denote a random variable having a Poisson distribution with parameter λ >0. Then
ProbX=k=e-λλkk! ,  k=0,1,2,
The mean and variance of the distribution are both equal to λ.
nag_poisson_dist (g01bkc) computes for given λ and k the probabilities:
plek=ProbXk pgtk=ProbX>k peqk=ProbX=k .
The method is described in Knüsel (1986).

4  References

Knüsel L (1986) Computation of the chi-square and Poisson distribution SIAM J. Sci. Statist. Comput. 7 1022–1036

5  Arguments

1:     rlamdadoubleInput
On entry: the parameter λ of the Poisson distribution.
Constraint: 0.0<rlamda106.
2:     kIntegerInput
On entry: the integer k which defines the required probabilities.
Constraint: k0.
3:     plekdouble *Output
On exit: the lower tail probability, ProbXk.
4:     pgtkdouble *Output
On exit: the upper tail probability, ProbX>k.
5:     peqkdouble *Output
On exit: the point probability, ProbX=k.
6:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT_ARG_LT
On entry, k=value.
Constraint: k0.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL_ARG_GT
On entry, rlamda=value.
Constraint: rlamda106.
NE_REAL_ARG_LE
On entry, rlamda=value.
Constraint: rlamda>0.0.

7  Accuracy

Results are correct to a relative accuracy of at least 10-6 on machines with a precision of 9 or more decimal digits, and to a relative accuracy of at least 10-3 on machines of lower precision (provided that the results do not underflow to zero).

8  Further Comments

The time taken by nag_poisson_dist (g01bkc) depends on λ and k. For given λ, the time is greatest when kλ, and is then approximately proportional to λ.

9  Example

This example reads values of λ and k from a data file until end-of-file is reached, and prints the corresponding probabilities.

9.1  Program Text

Program Text (g01bkce.c)

9.2  Program Data

Program Data (g01bkce.d)

9.3  Program Results

Program Results (g01bkce.r)


nag_poisson_dist (g01bkc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012