zipfPolylog {zipfextR}

The Zipf-Polylog Distribution (Zipf-Polylog).

Description

Probability mass function of the Zipf-Polylog distribution with parameters \alpha and \beta. The support of the Zipf-Polylog distribution are the strictly positive integer numbers large or equal than one.

Usage

dzipfpolylog(x, alpha, beta, log = FALSE, nSum = 1000)

pzipfpolylog(x, alpha, beta, log.p = FALSE, lower.tail = TRUE,
  nSum = 1000)

qzipfpolylog(p, alpha, beta, log.p = FALSE, lower.tail = TRUE,
  nSum = 1000)

rzipfpolylog(n, alpha, beta, nSum = 1000)

Arguments

x

Vector of positive integer values.

alpha

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

beta

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

log, log.p

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

nSum

The number of terms used for computing the Polylogarithm function (Default = 1000).

lower.tail

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

p

Vector of probabilities.

n

Number of random values to return.

Details

The probability mass function at a positive integer value x of the Zipf-Polylog distribution with parameters \alpha and \beta is computed as follows:

Value

dzipfpolylog gives the probability mass function

Examples

dzipfpolylog(1:10, 1.61, 0.98)
pzipfpolylog(1:10, 1.61, 0.98)
qzipfpolylog(0.8, 1.61, 0.98)