Likelihood inference for generalized Pareto distribution

A new methodological approach that enables the use of the maximum likelihood method in the Generalized Pareto Distribution is presented. Thus several models for the same data can be compared under Akaike and Bayesian information criteria. The view is based on a detailed theoretical study of the Generalized Pareto Distribution submodels with compact support.

[1]  Richard Lockhart,et al.  Methods to Distinguish Between Polynomial and Exponential Tails , 2011 .

[2]  Jin Zhang,et al.  A New and Efficient Estimation Method for the Generalized Pareto Distribution , 2009, Technometrics.

[3]  J. Hosking,et al.  Parameter and quantile estimation for the generalized pareto distribution , 1987 .

[4]  Tomasz J. Kozubowski,et al.  Testing Exponentiality Versus Pareto Distribution via Likelihood Ratio , 2008, Commun. Stat. Simul. Comput..

[5]  S. Grimshaw Computing Maximum Likelihood Estimates for the Generalized Pareto Distribution , 1993 .

[6]  AbuBakr S. Bahaj,et al.  A comparison of estimators for the generalised Pareto distribution , 2011 .

[7]  M. Meerschaert,et al.  Parameter Estimation for the Truncated Pareto Distribution , 2006 .

[8]  R. Brent Table errata: Algorithms for minimization without derivatives (Prentice-Hall, Englewood Cliffs, N. J., 1973) , 1975 .

[9]  J. Pickands Statistical Inference Using Extreme Order Statistics , 1975 .

[10]  S. Coles,et al.  An Introduction to Statistical Modeling of Extreme Values , 2001 .

[11]  Peter Hall,et al.  Bayesian likelihood methods for estimating the end point of a distribution , 2005 .

[12]  Seongjoo Song,et al.  A quantile estimation for massive data with generalized Pareto distribution , 2012, Comput. Stat. Data Anal..

[13]  Vartan Choulakian,et al.  Goodness-of-Fit Tests for the Generalized Pareto Distribution , 2001, Technometrics.

[14]  Russell C. H. Cheng,et al.  Estimating Parameters in Continuous Univariate Distributions with a Shifted Origin , 1983 .

[15]  Holger Rootzén,et al.  Extreme Values in Finance, Telecommunications, and the Environment , 2003 .

[16]  Jonathan A. Tawn,et al.  Extended generalised Pareto models for tail estimation , 2011, 1111.6899.

[17]  P. Embrechts,et al.  Quantitative Risk Management: Concepts, Techniques, and Tools , 2005 .

[18]  Richard L. Smith Maximum likelihood estimation in a class of nonregular cases , 1985 .

[19]  A. Hadi,et al.  Fitting the Generalized Pareto Distribution to Data , 1997 .

[20]  Ramesh C. Gupta,et al.  Residual coefficient of variation and some characterization results , 2000 .

[21]  Alberto Luceño,et al.  Fitting the generalized Pareto distribution to data using maximum goodness-of-fit estimators , 2006, Comput. Stat. Data Anal..

[22]  J. D. Castillo,et al.  Estimation of the generalized Pareto distribution , 2009 .

[23]  Mark E. J. Newman,et al.  Power-Law Distributions in Empirical Data , 2007, SIAM Rev..

[24]  Jin Zhang,et al.  LIKELIHOOD MOMENT ESTIMATION FOR THE GENERALIZED PARETO DISTRIBUTION , 2007 .

[25]  William R. Schucany,et al.  Robust and Efficient Estimation for the Generalized Pareto Distribution , 2004 .

[26]  Jin Zhang Improving on Estimation for the Generalized Pareto Distribution , 2010, Technometrics.

[27]  Russell C. H. Cheng,et al.  Corrected Maximum Likelihood in Non‐Regular Problems , 1987 .

[28]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[29]  PAUL EMBRECHTS,et al.  Modelling of extremal events in insurance and finance , 1994, Math. Methods Oper. Res..