GB2 (version 2.1.1)

Fisk: 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.

Value

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

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.

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

# NOT RUN {
library(laeken)
data(eusilc)

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

# Weights
w <- eusilc$rb050

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