zipfpss: The Zipf-Poisson Stop Sum Distribution (Zipf-PSS).

Description

Probability mass function, cumulative distribution function, quantile function and random number generation for the Zipf-PSS distribution with parameters \(\alpha\) and \(\lambda\). The support of the Zipf-PSS distribution are the positive integer numbers including the zero value. In order to work with its zero-truncated version the parameter isTruncated should be equal to True.

Usage

dzipfpss(x, alpha, lambda, log = FALSE, isTruncated = FALSE)
pzipfpss(q, alpha, lambda, log.p = FALSE, lower.tail = TRUE,
  isTruncated = FALSE)
rzipfpss(n, alpha, lambda, log.p = FALSE, lower.tail = TRUE,
  isTruncated = FALSE)
qzipfpss(p, alpha, lambda, log.p = FALSE, lower.tail = TRUE,
  isTruncated = FALSE)

Arguments

x, q

Vector of positive integer values.

alpha

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

lambda

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

log, log.p

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

isTruncated

Logical; if TRUE, the zero truncated version of the distribution is returned.

lower.tail

Logical; if TRUE (default), probabilities are \(P[X \leq x]\), otherwise, \(P[X > x]\).

Number of random values to return.

Vector of probabilities.

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.