laeken (version 0.4.3)

thetaMoment: Moment estimator

Description

Estimate the shape parameter of a Pareto distribution based on moments.

Usage

thetaMoment(x, k = NULL, x0 = NULL)

Arguments

x

a numeric vector.

k

the number of observations in the upper tail to which the Pareto distribution is fitted.

x0

the threshold (scale parameter) above which the Pareto distribution is fitted.

Value

• The estimated shape parameter.

Details

The arguments k and x0 of course correspond with each other. If k is supplied, the threshold x0 is estimated with the $n - k$ largest value in x, where $n$ is the number of observations. On the other hand, if the threshold x0 is supplied, k is given by the number of observations in x larger than x0. Therefore, either k or x0 needs to be supplied. If both are supplied, only k is used (mainly for back compatibility).

References

Dekkers, A.L.M., Einmahl, J.H.J. and de Haan, L. (1989) A moment estimator for the index of an extreme-value distribution. The Annals of Statistics, 17(4), 1833--1855.

See Also

paretoTail, fitPareto

Examples

data(eusilc)
# equivalized disposable income is equal for each household
# member, therefore only one household member is taken
eusilc <- eusilc[!duplicated(eusilc$db030),]

# estimate threshold
ts <- paretoScale(eusilc$eqIncome, w = eusilc$db090)

# using number of observations in tail
thetaMoment(eusilc$eqIncome, k = ts$k)

# using threshold
thetaMoment(eusilc$eqIncome, x0 = ts$x0)