laeken (version 0.5.3)

thetaTM: Trimmed mean estimator

Description

Estimate the shape parameter of a Pareto distribution using a trimmed mean approach.

Usage

thetaTM(x, k = NULL, x0 = NULL, beta = 0.05)

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.

beta

A numeric vector of length two giving the trimming proportions for the lower and upper end of the tail, respectively. If a single numeric value is supplied, it is recycled.

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

Brazauskas, V. and Serfling, R. (2000) Robust estimation of tail parameters for two-parameter Pareto and exponential models via generalized quantile statistics. Extremes, 3(3), 231--249.

Brazauskas, V. and Serfling, R. (2000) Robust and efficient estimation of the tail index of a single-parameter Pareto distribution. North American Actuarial Journal, 4(4), 12--27.

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

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