Generalizing the Pareto to the log-Pareto model and statistical inference |
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Authors: | Ulf Cormann Rolf-Dieter Reiss |
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Institution: | (1) Department of Mathematics, University of Siegen, Walter Flex Str. 3, 57068 Siegen, Germany |
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Abstract: | In this article we introduce a full-fledged statistical model of log-Pareto distribution functions (dfs) parametrized by two
shape parameters and a scale parameter. Pareto dfs can be regained in the limit by varying parameters of log-Pareto dfs, whence
the log-Pareto model can be regarded as an extension of the Pareto model. Log-Pareto dfs are first of all obtained by means
of exponential transformations of Pareto dfs. We also indicate an iterated application of such a procedure. A class of generalized
log-Pareto dfs is considered as well. In addition, power-pot (p-pot) stable dfs – related to p-max stable dfs – are introduced
and log-Pareto dfs are identified as special cases. A modification of a quick (systematic) estimator is proposed as an initial
estimator for the numerical computation of the maximum likelihood estimator (MLE) in the 3-parameter model.
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Keywords: | Pareto Log-Pareto and generalized log-Pareto dfs Exceedances Super-heavy tails P-max and p-pot stable dfs Quick estimators MLE Copepod data |
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