Learn R Programming

zipfextR (version 1.0.2)

zi_zipfpss: 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.