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

Author

Listed:
  • Marcelo Bourguignon

    (Departamento de Estatística, Universidade Federal do Rio Grande do Norte, Natal 59078-970, RN, Brazil)

  • Diego I. Gallardo

    (Departamento de Matemática, Facultad de Ingeniería, Universidad de Atacama, Copiapó 1530000, Chile)

  • Héctor J. Gómez

    (Departamento de Ciencias Matemáticas y Físicas, Facultad de Ingeniería, Universidad Católica de Temuco, Temuco 4780000, Chile)

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.

Suggested Citation

  • Marcelo Bourguignon & Diego I. Gallardo & Héctor J. Gómez, 2022. "A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters," Mathematics, MDPI, vol. 10(3), pages 1-8, February.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:528-:d:744349
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    References listed on IDEAS

    as
    1. Marcelo Bourguignon & Fernando Ferraz Nascimento, 2021. "Regression models for exceedance data: a new approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 157-173, March.
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    Cited by:

    1. Frederico Caeiro & Ayana Mateus, 2023. "A New Class of Generalized Probability-Weighted Moment Estimators for the Pareto Distribution," Mathematics, MDPI, vol. 11(5), pages 1-17, February.
    2. Saulius Paukštys & Jonas Šiaulys & Remigijus Leipus, 2023. "Truncated Moments for Heavy-Tailed and Related Distribution Classes," Mathematics, MDPI, vol. 11(9), pages 1-15, May.

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