zi_zipfpss {zipfextR}

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

Description

Probability mass function for the zero inflated Zipf-PSS distribution with parameters \alpha, \lambda and w. 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 \alpha parameter (\alpha > 1 ).

lambda

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

w

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

log

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

Details

The support of the \lambda parameter increases when the distribution is truncated at zero being \lambda \geq 0. It has been proved that when \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.