dpol {crandep}

Probability mass function (PMF) of Zipf-polylog distribution

Description

dpol returns the PMF at x for the Zipf-polylog distribution with parameters (alpha, theta). The distribution is reduced to the discrete power law when theta = 1.

Usage

dpol(x, alpha, theta, x_max = 100000L)

Arguments

x

Vector of positive integers

alpha

Real number greater than 1

theta

Real number in (0, 1]

x_max

Scalar (default 100000), positive integer limit for computing the normalising constant

Details

The PMF is proportional to x^(-alpha) * theta^x. It is normalised in order to be a proper PMF.

Value

A numeric vector of the same length as x

See Also

Spol for the corresponding survival function, dmix2 and dmix3 for the PMFs of the 2-component and 3-component discrete extreme value mixture distributions, respectively.

Examples

dpol(c(1,2,3,4,5), 1.2, 0.5)