HMMpa (version 1.0.2)

rgenpois: The Generalized Poisson Distribution

Description

Density, distribution function and random generation function for the generalized Poisson distribution.

Usage

rgenpois(n, lambda1, lambda2)

Value

rgenpois generates random deviates of the generalized Poisson distribution.

Arguments

n

number of observations

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

Author

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

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 \(\mbox{var}(X)=\frac{\lambda_1}{(1-\lambda_2)^3}\).

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, dgenpois; 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) )