Inference Based on Order Statistics from the Generalized Pareto Distribution and Application

ABSTRACT

In this article, we derive exact explicit expressions for the single, double, triple, and quadruple moments of order statistics from the generalized Pareto distribution (GPD). Also, we obtain the best linear unbiased estimates of the location and scale parameters (BLUE's) of the GPD. We then use these results to determine the mean, variance, and coefficients of skewness and kurtosis of certain linear functions of order statistics. These are then utilized to develop approximate confidence intervals for the generalized Pareto parameters using Edgeworth approximation and compare them with those based on Monte Carlo simulations. To show the usefulness of our results, we also present a numerical example. Finally, we give an application to real data.

Keywords:

• Approximate confidence interval
• BLUE's
• Coefficients of skewness and kurtosis
• Edgeworth approximation
• Moments
• Monte Carlo simulation
• Pivotal quantity

Mathematics Subject Classification:

• 62G32

Acknowledgments

The authors would like to thank the referees for their helpful comments, which improved the presentation of the article. The second author would like to thank the Research Center, College of Science, King Saud University, for funding the project (Stat/1422/27).