# paretoScale: Estimate the scale parameter of a Pareto distribution In laeken: Estimation of indicators on social exclusion and poverty

## Description

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

## Usage

 ```1 2``` ```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 first group member to appear are used for estimating the threshold (scale parameter). `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 implemented). `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 `"VanKerm"` (currently the only method implemented). `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 `"VanKerm"` (currently the only method implemented). `na.rm` a logical indicating whether missing values in `x` should be omitted.

## Details

Van Kerm's formula is given by

min(max(2.5 m(x), q(0.98)), q(0.97)),

where m(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.

## 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).

Andreas Alfons

## References

A. Alfons and M. Templ (2013) Estimation of Social Exclusion Indicators from Complex Surveys: The R Package laeken. Journal of Statistical Software, 54(15), 1–25. URL http://www.jstatsoft.org/v54/i15/

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.

`minAMSE`, `paretoQPlot`, `meanExcessPlot`
 ```1 2``` ```data(eusilc) paretoScale(eusilc\$eqIncome, eusilc\$db090, groups = eusilc\$db030) ```