A Median Regression Model to Estimate the Parameters of the Three-Parameter Generalized Pareto Distribution

Abstract

A regression procedure to estimate the parameters of the three-parameter generalized Pareto distribution is derived. The distribution function is transformed to a linear regression model where the dependent variable is in the Box-Cox transformed form. The profile likelihood approach assuming Laplace distributed disturbances and weighted least squares are used to estimate the parameters. The regression approach performs good in small samples with respect to efficiency. Two applications to estimate the index in peak over threshold problems are given.

Keywords:

• Generalized Pareto
• Median regression
• Least absolute deviation
• Laplace distribution

Mathematics Subject Classification:

• 62F10

Acknowledgment

I wish to thank an anonymous referee for drawing my attention to important research in this field, and for helpful suggestions.