A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters

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 propos...

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Bibliographic Details
Published in:Mathematics (Basel) 2022-02, Vol.10 (3), p.528
Main Authors: Bourguignon, Marcelo, Gallardo, Diego I., Gómez, Héctor J.
Format: Article
Language:English
Subjects:
Generalized linear models
Mathematics
modeling
Monte Carlo simulation
Parameter estimation
parameterization
pareto-type distributions
Random variables
Regression coefficients
Regression models
varying precision
Wealth distribution
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10030528