Fisk {GB2}R Documentation

Parameters of the Fisk Distribution

Description

Calculation of the parameters aa and bb of the Fisk distribution, which is a GB2 distribution with p=q=1p = q = 1. If mm and vv denote, respectively, the mean and variance of log(z)log(z), then a^=π/3v\hat{a} = \pi/\sqrt{3*v} and b^=exp(m)\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)log(z) and next the values of aa and bb under the Fisk distribution. Function fiskh first calculates the mean and variance of log(z)log(z), assuming a sample of households, and next the values of aa and bb under the Fisk distribution.

Value

fisk and fiskh return vectors of length 4 containing the estimated parameters aa, eqnb, as well as p=1p=1 and q=1q=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)

[Package GB2 version 2.1.1 Index]