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The Logistic Burr XII Distribution: Properties and Applications to Income Data

Author

Listed:
  • Renata Rojas Guerra

    (Department of Statistics, Centro de Ciências Naturais e Exatas, Universidade Federal de Santa Maria, Santa Maria 97105-900, Brazil)

  • Fernando A. Peña-Ramírez

    (Department of Statistics, Facultad de Ciencias, Universidad Nacional de Colombia, Bogotá 11001, Colombia)

  • Gauss M. Cordeiro

    (Department of Statistics, Centro de Ciências Exatas e da Natureza, Universidade Federal de Pernambuco, Recife 50670-901, Brazil)

Abstract

We define and study the four-parameter logistic Burr XII distribution. It is obtained by inserting the three-parameter Burr XII distribution as the baseline in the logistic-X family and may be a useful alternative method to model income distribution and could be applied to other areas. We illustrate that the new distribution can have decreasing and upside-down-bathtub hazard functions and that its density function is an infinite linear combination of Burr XII densities. Some mathematical properties of the proposed model are determined, such as the quantile function, ordinary and incomplete moments, and generating function. We also obtain the maximum likelihood estimators of the model parameters and perform a Monte Carlo simulation study. Further, we present a parametric regression model based on the introduced distribution as an alternative to the location-scale regression model. The potentiality of the new distribution is illustrated by means of two applications to income data sets.

Suggested Citation

  • Renata Rojas Guerra & Fernando A. Peña-Ramírez & Gauss M. Cordeiro, 2023. "The Logistic Burr XII Distribution: Properties and Applications to Income Data," Stats, MDPI, vol. 6(4), pages 1-20, November.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:4:p:78-1279:d:1284741
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    References listed on IDEAS

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    1. Pedro Rafael D Marinho & Rodrigo B Silva & Marcelo Bourguignon & Gauss M Cordeiro & Saralees Nadarajah, 2019. "AdequacyModel: An R package for probability distributions and general purpose optimization," PLOS ONE, Public Library of Science, vol. 14(8), pages 1-30, August.
    2. Paranaíba, Patrícia F. & Ortega, Edwin M.M. & Cordeiro, Gauss M. & Pescim, Rodrigo R., 2011. "The beta Burr XII distribution with application to lifetime data," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1118-1136, February.
    3. Ayman Alzaatreh & Carl Lee & Felix Famoye, 2013. "A new method for generating families of continuous distributions," METRON, Springer;Sapienza Università di Roma, vol. 71(1), pages 63-79, June.
    4. Katikas, Loukas & Dimitriadis, Panayiotis & Koutsoyiannis, Demetris & Kontos, Themistoklis & Kyriakidis, Phaedon, 2021. "A stochastic simulation scheme for the long-term persistence, heavy-tailed and double periodic behavior of observational and reanalysis wind time-series," Applied Energy, Elsevier, vol. 295(C).
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