zipfextR (version 1.0.2)

zipfpeMoments: Distribution Moments.

Description

General function to compute the k-th moment of the Zipf-PE distribution for any integer value \(k \geq 1\), when it exists. The k-th moment exists if and only if \(\alpha > k + 1\). For k = 1, this function returns the same value as the zipfpeMean function.

Usage

zipfpeMoments(k, alpha, beta, tolerance = 10^(-4))

Arguments

k

Order of the moment to compute.

alpha

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

beta

Value of the \(\beta\) parameter (\(\beta \in (-\infty, +\infty)\)).

tolerance

Tolerance used in the calculations (default = \(10^{-4}\)).

Value

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

Details

The k-th moment of the Zipf-PE distribution is finite for \(\alpha\) values strictly greater than \(k + 1\). 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.

Examples

# NOT RUN {
zipfpeMoments(3, 4.5, 1.3)
zipfpeMoments(3, 4.5, 1.3,  1*10^(-3))
# }