laeken (version 0.4.3)

paretoScale: Estimate the scale parameter of a Pareto distribution

Description

Estimate the scale parameter of a Pareto distribution, i.e., the threshold for Pareto tail modeling.

Usage

paretoScale(x, w = NULL, groups = NULL,
    method = "VanKerm", center = c("mean", "median"),
    probs = c(0.97, 0.98), na.rm = FALSE)

Arguments

x

a numeric vector.

w

an optional numeric vector giving sample weights.

groups

an optional vector or factor specifying groups of elements of x (e.g., households). If supplied, each group of observations is expected to have the same value in x (e.g., household income). Only the values of every f

method

a character string specifying the estimation method. If "VanKerm", Van Kerm's method is used, which is a rule of thumb specifically designed for the equivalized disposable income in EU-SILC data (currently the only method impleme

center

a character string specifying the estimation method for the center of the distribution. Possible values are "mean" for the weighted mean and "median" for the weighted median. This is used if method is

probs

a numeric vector of length two giving probabilities to be used for computing weighted quantiles of the distribution. Values should be close to 1 such that the quantiles correspond to the upper tail. This is used if method is

na.rm

a logical indicating whether missing values in x should be omitted.

Value

• An object of class "paretoScale" with the following components:
• x0
  the threshold (scale parameter).
• k
  the number of observations in the tail (i.e., larger than the threshold).

Details

Van Kerm's formula is given by $$\min(\max(2.5 \bar{x}, q(0.98), q(0.97))),$$ where $\bar{x}$ denotes the weighted mean and $q(.)$ denotes weighted quantiles. This function allows to compute generalizations of Van Kerm's formula, where the mean can be replaced by the median and different quantiles can be used.

References

Van Kerm, P. (2007) Extreme incomes and the estimation of poverty and inequality indicators from EU-SILC. IRISS Working Paper Series 2007-01, CEPS/INSTEAD.

See Also

minAMSE, paretoQPlot, meanExcessPlot

Examples

data(eusilc)
paretoScale(eusilc$eqIncome, eusilc$db090, groups = eusilc$db030)