dmoezipf: Density function.

In moezipfR: Marshall-Olkin Extended Zipf

Description

Density function for the Marshall-Olkin Extended Zipf distribution with parameters α and β.

Usage

dmoezipf(x, alpha, beta, log = FALSE, show.plot = F)

Arguments

x	Vector of positive integer values.
alpha	Value of the α parameter (α > 1 ).
beta	Value of the β parameter (β > 0 ).
log	Logical; if TRUE, probabilities p are given as log(p).
show.plot	Logical; if TRUE shows the plot of the distibution (default = FALSE).

Details

The probability mass function at a positive integer value x of the MOEZipf distribution with parameters α and β is computed as follows:

p(x | α, β) = \frac{x^{-α} β ζ(α) }{[ζ(α) - \bar{β} ζ (α, x)] [ζ (α) - \bar{β} ζ (α, x + 1)]}, α > 1, β > 0,

where ζ(α) is the Riemann-zeta function at α, ζ(α, x) is the Hurtwitz zeta function with arguments α and x, and \bar{β} = 1 - β.

Value

The probability associated to each value in vector x.

Examples

dmoezipf(1:10, 2.5, 1.3)
dmoezipf(1:10, 2.5, 1.3, show.plot = TRUE)

moezipfR documentation built on May 2, 2019, 3:25 a.m.