NAG CL Interface
g01bkc (prob_​poisson)

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1 Purpose

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

2 Specification

#include <nag.h>
void  g01bkc (double rlamda, Integer k, double *plek, double *pgtk, double *peqk, NagError *fail)
The function may be called by the names: g01bkc, nag_stat_prob_poisson or nag_poisson_dist.

3 Description

Let X denote a random variable having a Poisson distribution with parameter λ (>0). Then
Prob{X=k}=e-λλkk! ,  k=0,1,2,  
The mean and variance of the distribution are both equal to λ.
g01bkc computes for given λ and k the probabilities:
plek=Prob{Xk} pgtk=Prob{X>k} peqk=Prob{X=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: rlamda double Input
On entry: the parameter λ of the Poisson distribution.
Constraint: 0.0<rlamda106.
2: k Integer Input
On entry: the integer k which defines the required probabilities.
Constraint: k0.
3: plek double * Output
On exit: the lower tail probability, Prob{Xk}.
4: pgtk double * Output
On exit: the upper tail probability, Prob{X>k}.
5: peqk double * Output
On exit: the point probability, Prob{X=k}.
6: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument value had an illegal value.
On entry, k=value.
Constraint: k0.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
On entry, rlamda=value.
Constraint: rlamda106.
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 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
g01bkc is not threaded in any implementation.

9 Further Comments

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

10 Example

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

10.1 Program Text

Program Text (g01bkce.c)

10.2 Program Data

Program Data (g01bkce.d)

10.3 Program Results

Program Results (g01bkce.r)