zi_zipfpss {zipfextR}R Documentation

The Zero Inflated Zipf-Poisson Stop Sum Distribution (ZI Zipf-PSS).

Description

Probability mass function for the zero inflated Zipf-PSS distribution with parameters α\alpha, λ\lambda and ww. The support of thezero inflated Zipf-PSS distribution are the positive integer numbers including the zero value.

Usage

d_zi_zipfpss(x, alpha, lambda, w, log = FALSE)

Arguments

x

Vector of positive integer values.

alpha

Value of the α\alpha parameter (α>1\alpha > 1 ).

lambda

Value of the λ\lambda parameter (λ>0\lambda > 0 ).

w

Value of the ww parameter (0 < w<1w < 1 ).

log

Logical; if TRUE, probabilities p are given as log(p).

Details

The support of the λ\lambda parameter increases when the distribution is truncated at zero being λ0\lambda \geq 0. It has been proved that when λ=0\lambda = 0 one has the degenerated version of the distribution at one.

References

Panjer, H. H. (1981). Recursive evaluation of a family of compound distributions. ASTIN Bulletin: The Journal of the IAA, 12(1), 22-26.

Sundt, B., & Jewell, W. S. (1981). Further results on recursive evaluation of compound distributions. ASTIN Bulletin: The Journal of the IAA, 12(1), 27-39.


[Package zipfextR version 1.0.2 Index]