This function evaluates the Poisson probability density function.

Function Return Value

POIPR — Function value, the probability that a Poisson random variable takes a value equal to K.   (Output)

Required Arguments

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

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

FORTRAN 90 Interface

Generic:                              POIPR (K, THETA)

Specific:                             The specific interface names are S_POIPR and D_POIPR.

FORTRAN 77 Interface

Single:                                POIPR (K, THETA)

Double:                              The double precision name is DPOIPR.

Description

The function POIPR evaluates the probability density 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−θθk/k!,       for k = 0, 1, 2,…

POIPR evaluates this function directly, taking logarithms and using the log gamma function.

Figure 11- 5  Poisson Probability Function

Comments

Informational error

Type Code

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 probability function at 7.

 

      USE UMACH_INT

      USE POIPR_INT

      IMPLICIT   NONE

 

      INTEGER    K, NOUT

      REAL       PR, THETA

!

      CALL UMACH (2, NOUT)

      K     = 7

      THETA = 10.0

      PR    = POIPR(K,THETA)

      WRITE (NOUT,99999) PR

99999 FORMAT (' The probability that X is equal to 7 is ', F6.4)

      END

Output

 

The probability that X is equal to 7 is 0.0901

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