zipfextR (version 1.0.2)

zipfPolylog: 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.

Value

dzipfpolylog gives the probability mass function

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:

Examples

# NOT RUN {
dzipfpolylog(1:10, 1.61, 0.98)
pzipfpolylog(1:10, 1.61, 0.98)
qzipfpolylog(0.8, 1.61, 0.98)
# }