moezipfR.moments: Distribution Moments.

In moezipfR: Marshall-Olkin Extended Zipf

Description

General function to compute the k-th moment of the distribution, for any k ≥q 1 when it exists. Note that the k-th moment exists if and only if α > k + 1. When k = 1, this function returns the same value as the moezipfR.mean function.

Usage

moezipfR.moments(k, alpha, beta, tolerance = 10^(-4))

Arguments

k	Order of the moment to compute.
alpha	Value of the α parameter (α > k + 1).
beta	Value of the β parameter (β > 0).
tolerance	Tolerance used in the calculations (default = 10^{-4}).

Details

The k-th moment of the MOEZipf distribution is finite for α values strictly greater than k + 1. For a random variable Y that follows a MOEZipf distribution with parameters α and β, the k-th moment is computed as:

E(Y^k) = ∑_{x = 1} ^∞ \frac{β ζ(α) x^{-α + k}}{[ζ(α) - \bar{β}ζ(α, x)][ζ(α) - \bar{β}ζ(α, x + 1)]}\,, α ≥q k + 1\,, β > 0

The k-th moment is computed calculating the partial sums of the serie, and it stops when two consecutive partial sums differs less than the tolerance value. The last partial sum is returned.

Value

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

Examples

moezipfR.moments(3, 4.5, 1.3)
moezipfR.moments(3, 4.5, 1.3,  1*10^(-3))

moezipfR documentation built on May 2, 2019, 3:25 a.m.