moezipfR.mean: Expected value.

In moezipfR: Marshall-Olkin Extended Zipf

Description

Computes the expected value of the MOEZipf distribution for given values of parameters α and β.

Usage

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

Arguments

alpha	Value of the α parameter (α > 2).
beta	Value of the β parameter (β > 0).
tolerance	Tolerance used in the calculations (default = 10^{-4}).

Details

The expected value of the MOEZipf distribution only exists for α values strictly greater than 2. In this case, if Y is a random variable that follows a MOEZipf distribution with parameters α and β, the expected value is computed as:

E(Y) = ∑_{x = 1} ^∞ \frac{β ζ(α) x^{-α + 1}}{[ζ(α) - \bar{β}ζ(α, x)][ζ(α) - \bar{β}ζ(α, x + 1)]}\,, α > 2\,, β > 0

The mean 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 mean value of the distribution.

Examples

moezipfR.mean(2.5, 1.3)
moezipfR.mean(2.5, 1.3, 10^(-3))

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