Fisk: Parameters of the Fisk Distribution

In GB2: Generalized Beta Distribution of the Second Kind: Properties, Likelihood, Estimation

Parameters of the Fisk Distribution

Description

Calculation of the parameters a and b of the Fisk distribution, which is a GB2 distribution with p = q = 1. If m and v denote, respectively, the mean and variance of log(z), then \hat{a} = \pi/\sqrt{3*v} and \hat{b} = \exp(m).

Usage

fisk(z, w=rep(1, length(z)))
fiskh(z, w=rep(1, length(z)), hs=rep(1, length(z)))

Arguments

z	numeric; vector of data values.
w	numeric; vector of weights. Must have the same length as z. By default w is a vector of 1.
hs	numeric; vector of household sizes. Must have the same length as z. By default hs is a vector of 1.

Details

Function fisk first calculates the mean and variance of log(z) and next the values of a and b under the Fisk distribution. Function fiskh first calculates the mean and variance of log(z), assuming a sample of households, and next the values of a and b under the Fisk distribution.

Value

fisk and fiskh return vectors of length 4 containing the estimated parameters a, b, as well as p=1 and q=1.

Author(s)

Monique Graf

References

Graf, M., Nedyalkova, D., Muennich, R., Seger, J. and Zins, S. (2011) AMELI Deliverable 2.1: Parametric Estimation of Income Distributions and Indicators of Poverty and Social Exclusion. Technical report, AMELI-Project.

See Also

optim for the general-purpose optimization

Examples

library(laeken)
data(eusilc)

# Income
inc <- as.vector(eusilc$eqIncome)

# Weights
w <- eusilc$rb050

#Fisk parameters
fpar <- fisk(inc, w)

GB2 documentation built on Aug. 21, 2025, 6:03 p.m.