pgenpois: The Generalized Poisson Distribution

In HMMpa: Analysing Accelerometer Data Using Hidden Markov Models

The Generalized Poisson Distribution

Description

Distribution function for the generalized Poisson distribution.

Usage

pgenpois(q, lambda1, lambda2)

Arguments

q	a numeric vector of quantiles
lambda1	a single numeric value for parameter lambda1 with lambda1 > 0
lambda2	a single numeric value for parameter lambda2 with 0 \le lamdba2 < 1. When lambda2=0, the generalized Poisson distribution reduces to the Poisson distribution

Details

The generalized Poisson distribution has the density

p(x) = \lambda_1 (\lambda_1 + \lambda_2 \cdot x)^{x-1} \frac{ \exp(-\lambda_1-\lambda_2 \cdot x) )}{x!}

for x = 0,1,2,\ldots,b with \mbox{E}(X)= \frac{\lambda_1}{1-\lambda_2} and variance \mbox{var}(X)=\frac{\lambda_1}{(1-\lambda_2)^3}.

Value

pgenpois gives the distribution function of the generalized Poisson distribution.

Author(s)

Based on Joe and Zhu (2005). Implementation by Vitali Witowski (2013).

References

Joe, H., Zhu, R. (2005). Generalized poisson distribution: the property of mixture of poisson and comparison with negative binomial distribution. Biometrical Journal 47(2):219–229.

See Also

pgenpois, rgenpois; Distributions for other standard distributions, including dpois for the Poisson distribution.

Examples

dgenpois(x = seq(0,20), lambda1 = 10, lambda2 = 0.5) 
pgenpois(q = 5, lambda1 = 10, lambda2 = 0.5) 
hist(rgenpois(n = 1000, lambda1 = 10, lambda2 = 0.5) )

HMMpa documentation built on April 3, 2025, 10:29 p.m.