Abstract
Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression models where the response variable is Pareto-type distributed using new parameterizations that are indexed by mean and precision parameters. The main motivation for these new parametrizations is the useful interpretation of the regression coefficients in terms of the mean and precision, as is usual in the context of regression models. The parameter estimation of these new models is performed, based on the maximum likelihood paradigm. Some numerical illustrations of the estimators are presented with a discussion of the obtained results. Finally, we illustrate the practicality of the new models by means of two applications to real data sets.
Highlights
The Pareto distribution was originally applied by Pareto [1] to model the unequal distribution of wealth
The random variable Y has the Pareto distribution if its cumulative distribution function (CDF) for y ≥ β is given by Academic Editor: Simeon Reich
Despite the nice properties of Pareto-type distributions, none of their parameters correspond to the expectation, which complicates the interpretation of regression models specified using these distributions
Summary
The Pareto distribution was originally applied by Pareto [1] to model the unequal distribution of wealth. The parameter β is only a scale factor, which is known as the tail index When this distribution is used to model the distribution of wealth, the parameter α a is called the Pareto index. Despite the nice properties of Pareto-type distributions, none of their parameters correspond to the expectation, which complicates the interpretation of regression models specified using these distributions. In this context, we proposed a new parameterization of these distributions that is indexed by mean and precision parameters. Concluding remarks and possible points for future research are given in the Section 5
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