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Estimation of the shape parameter of a generalized Pareto distribution based on a transformation to Pareto distributed variables

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  • J. Martin van Zyl

Abstract

Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using transformed observations, based on the probability weighted method is tested. It was found to improve the performance of the probability weighted estimator and performs good with respect to bias and MSE.

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  • J. Martin van Zyl, 2012. "Estimation of the shape parameter of a generalized Pareto distribution based on a transformation to Pareto distributed variables," Papers 1210.7642, arXiv.org, revised Dec 2012.
    • Handle: RePEc:arx:papers:1210.7642
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    1. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    2. del Castillo, Joan & Daoudi, Jalila, 2009. "Estimation of the generalized Pareto distribution," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 684-688, March.
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