laeken (version 0.5.3)

thetaQQ: QQ-estimator

Description

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

Usage

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

Value

The estimated shape parameter.

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.

Author

Andreas Alfons and Josef Holzer

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

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)