zipfpss {zipfextR}

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].

n

Number of random values to return.

p

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.