poissonCdf¶

Evaluates the Poisson distribution function.

Synopsis¶

poissonCdf (k, theta)

Required Arguments¶

int k (Input): Argument for which the Poisson distribution function is to be evaluated.
float theta (Input): Mean of the Poisson distribution. Argument theta must be positive.

Return Value¶

The probability that a Poisson random variable takes a value less than or equal to k.

Description¶

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

$f(x) = e^{-q} θ^x/x!, for x = 0, 1, 2, …$

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

$f(x + 1) = f(x)q/(x + 1), for x = 0, 1, 2, …, k - 1$

with $f(0)=e^{-q}$ .

Figure 9.24 — Plot of $F_p(k,\theta)$

Example¶

Suppose X is a Poisson random variable with $\theta=10$ . This example evaluates the probability that $X\leq 7$ .

from __future__ import print_function
from numpy import *
from pyimsl.math.poissonCdf import poissonCdf

k = 7
theta = 10.0

p = poissonCdf(k, theta)
print("Pr(x <= 7) = %6.4f" % (p))

Output¶

Pr(x <= 7) = 0.2202

Informational Errors¶

IMSL_LESS_THAN_ZERO The input argument, k, is less than zero.