dbetapoisson: Probability function of Beta-Poisson mixture distribution

In cbaumbach/betapoisson: Beta-Poisson Mixture Distribution

Description

Probability function of Beta-Poisson mixture distribution

Usage

dbetapoisson(x, a, b, lambda = 1)

Arguments

x	vector of (non-negative integer) quantiles
a, b	parameters of mixing Beta distribution
lambda	Poisson mean before thinning (see Details)

Details

The Beta-Poisson distribution with parameters a, b, and lambda, can be understood as a random variable constructed by independent p-thinning (see Definition 2.4 in reference 1) from a Poisson random variable with mean lambda where p itself is a random variable following a Beta distribution with parameters a and b.

The expected value and variance of X can be written as follows (see reference 2):

E(X) = E(lambda) = a/(a+b)

V(X) = E(lambda) + V(lambda) = a/(a+b) + (ab)/((a+b)^2(a+b+1))

where lambda has a Beta distribution with parameters a and b.

References

1. Jan Grandell, Mixed Poisson Processes, CRC Press, 1997, pages 43 ff.

2. Dimitris Karlis and Evdokia Xekalaki, Mixed Poisson Distributions, International Statistical Review (2005), *73*, 1, 35-58

cbaumbach/betapoisson documentation built on May 13, 2019, 1:47 p.m.