Resource title

Some Convergence Problems On Heavy Tail Estimation Using Upper Order Statistics For Generalized Pareto and Lognormal Distributions

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Resource description

In some applications, the population characteristics of main interest can be found in the tails of the distribution function. The study of risk of extreme events will lead to the use of probability distributions and the scenarios that correspond to the tail of these distributions. Considering two approaches: parametric and nonparametric, the research emphasizes the assessment of distribution tails, assuming that underlying distributions are heavy tailed. Two heavy tailed distributions are considered: Generalized Pareto and Lognormal. The Maximum likelihood estimation method, using the complete sample, and using only the upper order statistics provide estimators of the parameters. Measures of Bias and Mean Squared Error of the estimators of the parameters, and the Conditional Mean Exceedence Functions of the distributions, are generated. The methodology for estimating population parameters, has potential applications in financial markets, quality control, assurance portfolios, monitoring of residual discharges, medical applications, design of environmental policies, or calibration and adjustment of processes and equipment. The main idea is to present, and analyze the methods used for the estimation, and some convergence problems when these two distribution functions are used in generating scenarios.

Resource author

Raul Hernandez-Molinar, John Lefante

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Resource publish date

Resource language

eng

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text/html

Resource resource URL

http://hdl.handle.net/10419/22245

Resource license

Adapt according to the presented license agreement and reference the original author.