zipfpolylogMoments: Moments of the Zipf-Polylog Distribution.

In zipfextR: Zipf Extended Distributions

Description

General function to compute the k-th moment of the ZipfPolylog distribution for any integer value k ≥q 1, when it exists. #' For k = 1, this function returns the same value as the zipfpolylogMean function.

Usage

zipfpolylogMoments(k, alpha, beta, tolerance = 10^(-4), nSum = 1000)

Arguments

k	Order of the moment to compute.
alpha	Value of the α parameter (α > k + 1).
beta	Value of the β parameter (β \in (-∞, +∞)).
tolerance	Tolerance used in the calculations (default = 10^{-4}).
nSum	The number of terms used for computing the Polylogarithm function (default = 1000).

Details

The k-th moment of the Zipf-Polylog distribution is always finite, but, for α >1 and β = 0 the k-th moment is only finite for all α > k + 1. It is computed by calculating the partial sums of the serie, and stopping when two consecutive partial sums differ less than the tolerance value. The value of the last partial sum is returned.

Value

A positive real value corresponding to the k-th moment of the distribution.

Examples

zipfpolylogMoments(1, 0.2, 0.90)
zipfpolylogMoments(3, 4.5, 0.90,  1*10^(-3))

zipfextR documentation built on July 8, 2020, 6:23 p.m.