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An Alternative Lambert-Type Distribution for Bounded Data

Author

Listed:
  • Héctor Varela

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Mario A. Rojas

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Jimmy Reyes

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

  • Yuri A. Iriarte

    (Departamento de Matemáticas, Facultad de Ciencias Básicas, Universidad de Antofagasta, Antofagasta 1240000, Chile
    These authors contributed equally to this work.)

Abstract

In this article, we propose a new two-parameter distribution for bounded data such as rates, proportions, or percentages. The density function of the proposed distribution, presenting monotonic, unimodal, and inverse-unimodal shapes, tends to a positive finite value at the lower end of its support, which can lead to a better fit of the lower empirical quantiles. We derive some of the main structural properties of the new distribution. We make a description of the skewness and kurtosis of the distribution. We discuss the parameter estimation under the maximum likelihood method. We developed a simulation study to evaluate the behavior of the estimators. Finally, we present two applications to real data providing evidence that the proposed distribution can perform better than the popular beta and Kumaraswamy distributions.

Suggested Citation

  • Héctor Varela & Mario A. Rojas & Jimmy Reyes & Yuri A. Iriarte, 2023. "An Alternative Lambert-Type Distribution for Bounded Data," Mathematics, MDPI, vol. 11(3), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:3:p:667-:d:1049583
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    References listed on IDEAS

    as
    1. Yuri A. Iriarte & Mário de Castro & Héctor W. Gómez, 2020. "The Lambert- F Distributions Class: An Alternative Family for Positive Data Analysis," Mathematics, MDPI, vol. 8(9), pages 1-17, August.
    2. Richard Blundell & Alan Duncan & Krishna Pendakur, 1998. "Semiparametric estimation and consumer demand," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(5), pages 435-461.
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