dgenpois function

The Generalized Poisson Distribution

Density function for the generalized Poisson distribution.

dgenpois(x, lambda1, lambda2)

Arguments

• x: a vector of (non-negative integer) 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

Returns

dgenpois gives the density of the generalized Poisson distribution.

Details

The generalized Poisson distribution has the density

for $x = 0,1,2,\ldots$,b with $E(x)=lambda1/(1-lambda2)$ and variance $var(x)=lambda1/(1-lambda2)^3$.

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) )

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.

Author(s)

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