zipfpssMean: Expected value of the Zipf-PSS distribution.

In zipfextR: Zipf Extended Distributions

Description

Computes the expected value of the Zipf-PSS distribution for given values of parameters α and λ.

Usage

zipfpssMean(alpha, lambda, isTruncated = FALSE)

Arguments

alpha	Value of the α parameter (α > 2).
lambda	Value of the λ parameter (λ > 0).
isTruncated	Logical; if TRUE Use the zero-truncated version of the distribution to calculate the expected value (default = FALSE).

Details

The expected value of the Zipf-PSS distribution only exists for α values strictly greater than 2. The value is obtained from the law of total expectation that says that:

E[Y] = E[N]\, E[X],

where E[X] is the mean value of the Zipf distribution and E[N] is the expected value of a Poisson one. From where one has that:

E[Y] = λ\, \frac{ζ(α - 1)}{ζ(α)}

Particularlly, if one is working with the zero-truncated version of the Zipf-PSS distribution. This values is computed as:

E[Y^{ZT}] = \frac{λ\, ζ(α - 1)}{ζ(α)\, (1 - e^{-λ})}

Value

A positive real value corresponding to the mean value of the distribution.

References

Sarabia Alegría, J. M., Gómez Déniz, E. M. I. L. I. O., & Vázquez Polo, F. (2007). Estadística actuarial: teoría y aplicaciones. Pearson Prentice Hall.

Examples

zipfpssMean(2.5, 1.3)
zipfpssMean(2.5, 1.3, TRUE)

Example output

[1] 2.531584
[1] 3.479993

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