*! version 1.0.0 24jul2010

help nrpecMichal Brzezinski (July 2010)

Title

nrpec -- Estimate the number (k) of extreme order statistics used for fitting the Pareto model to upper tails of distributions

Syntax

nrpec [varname] [, options]

k(scalar) the maximum number of extreme order statistics used in estimation

x0(scalar) the minimum value of varname used in estimation

If neither k nor x0 options are used, nrpec searches for optimal k over the whole range of varname.

Description

nrpec estimates the number k of extreme ordered statistics
(e.g. highest incomes) for fitting the Pareto model to the upper tail of the distribution.
It uses the (non-robust) Pareto error criterion (C-criterion) introduced
in Dupuis and Victoria-Feser (2006).
Estimating k is equivalent to estimating the scale parameter x0 of the Pareto distribution:
k = SUM I(varname >= x0), where I is the indicator function. The estimated x0 can be then used in fitting Pareto model by, e.g., ML method, see paretofit.

For an implementation of Pareto error criterion for choosing k, also introduced in Dupuis and Victoria-Feser (2006), which is robust to extreme observations, see rpec, if installed.

Examples

To search for optimal k over the whole range of varname:

. nrpec varname

To search for optimal k among the 50 largest values of varname

. nrpec varname, k(50)

To search for optimal k among the values of varname >= 10000

. nrpec varname, x0(10000)

References

Dupuis, Debbie J. and Victoria-Feser, Maria-Pia (2006). A Robust Prediction Error Criterion for Pareto Modelling of Upper Tails. The Canadian Journal of Statistics, 34 (4), 639-658.

Also see

Online: help for rpec, paretofit, hillp if installed.

Author

Michal Brzezinski <mbrzezinski@wne.uw.edu.pl>, Faculty of Economic Sciences, University of Warsaw, Poland.