thetaQQ: QQ-estimator

In aalfons/laeken: Estimation of Indicators on Social Exclusion and Poverty

QQ-estimator

Description

Estimate the shape parameter of a Pareto distribution using a quantile-quantile approach.

Usage

thetaQQ(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.

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).

Value

The estimated shape parameter.

Note

The argument x0 for the threshold (scale parameter) of the Pareto distribution was introduced in version 0.2.

Author(s)

Andreas Alfons and Josef Holzer

References

Kratz, M.F. and Resnick, S.I. (1996) The QQ-estimator and heavy tails. Stochastic Models, 12(4), 699–724.

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
thetaQQ(eusilc$eqIncome, k = ts$k)

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

aalfons/laeken documentation built on Feb. 9, 2024, 7:16 p.m.