1. A goodness-of-fit statistic for Pareto-type behaviour
- Author
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Beirlant, Jan, de Wet, Tertius, and Goegebeur, Yuri
- Subjects
- *
CLUSTER analysis (Statistics) , *MATHEMATICAL statistics , *RANDOM variables , *MATHEMATICAL variables - Abstract
Abstract: The fit of a statistical model can be visually assessed by inspection of a quantile–quantile or QQ plot. For the strict Pareto distribution, since log-transformed Pareto random variables are exponentially distributed, it is natural to consider an exponential quantile plot based on the log-transformed data. In case the data originate from a Pareto-type distribution, the Pareto quantile plot will be linear but only in some of the largest observations. In this paper we modify the Jackson statistic, originally proposed as a goodness-of-fit statistic for testing exponentiality, in such a way that it measures the linearity of the k largest observations on the Pareto quantile plot. Further, by taking the second-order tail behaviour of a Pareto-type model into account we construct a bias-corrected Jackson statistic. For both statistics the limiting distribution is derived. Next to these asymptotic results we also evaluate the small sample behaviour on the basis of a simulation study. The method is illustrated on two practical case studies. [Copyright &y& Elsevier]
- Published
- 2006
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