POIDF

This function evaluates the Poisson cumulative distribution function.

Function Return Value

POIDF — Function value, the probability that a Poisson random variable takes a value less than or equal to K. (Output)

Required Arguments

K — Argument for which the Poisson cumulative distribution function is to be evaluated. (Input)

THETA — Mean of the Poisson distribution. (Input)
THETA must be positive.

FORTRAN 90 Interface

Generic: POIDF (K, THETA)

Specific: The specific interface names are S_POIDF and D_POIDF.

FORTRAN 77 Interface

Single: POIDF (K, THETA)

Double: The double precision name is DPOIDF.

Description

The function POIDF evaluates the cumulative distribution function of a Poisson random variable with parameter THETA. THETA, which is the mean of the Poisson random variable, must be positive. The probability function (with θ = THETA) is

f(x) = e−θθx/x!,      for x = 0, 1, 2, …

The individual terms are calculated from the tails of the distribution to the mode of the distribution and summed. POIDF uses the recursive relationship

f(x + 1) = f(x)θ/(x + 1),      for x = 0, 1, 2, …k – 1,

with f(0) = e−θ.

Comments

Informational Error

 

Type	Code	Description
1	1	The input argument, K, is less than zero.

Example

Suppose X is a Poisson random variable with θ = 10. In this example, we evaluate the distribution function at 7.

 

USE UMACH_INT

USE POIDF_INT

IMPLICIT NONE

INTEGER K, NOUT

REAL DF, THETA

!

CALL UMACH (2, NOUT)

K = 7

THETA = 10.0

DF = POIDF(K,THETA)

WRITE (NOUT,99999) DF

99999 FORMAT (' The probability that X is less than or equal to ', &

'7 is ', F6.4)

END

Output

 

The probability that X is less than or equal to 7 is 0.2202