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

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  • Hernandez-Molinar, Raul
  • Lefante, John

Abstract

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.

Suggested Citation

  • Hernandez-Molinar, Raul & Lefante, John, 2003. "Some Convergence Problems On Heavy Tail Estimation Using Upper Order Statistics For Generalized Pareto and Lognormal Distributions," SFB 373 Discussion Papers 2003,30, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  • Handle: RePEc:zbw:sfb373:200330
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    1. Judge, G. G. & Hill, R. Carter & Bock, M. E., 1990. "An adaptive empirical Bayes estimator of the multivariate normal mean under quadratic loss," Journal of Econometrics, Elsevier, vol. 44(1-2), pages 189-213.
    2. Golan, Amos & Judge, George G. & Miller, Douglas, 1996. "Maximum Entropy Econometrics," Staff General Research Papers Archive 1488, Iowa State University, Department of Economics.
    3. Miller, D. & Golan, Amos & Judge, G., 1998. "Information Recovery in Simultaneous Equation Statistical Models," Staff General Research Papers Archive 1319, Iowa State University, Department of Economics.
    4. Golan, Amos & Judge, G. & Miller, D., 1997. "The Maximum Entropy Approach to Estimation and Inference: An Overview," Staff General Research Papers Archive 1327, Iowa State University, Department of Economics.
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