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Some Extensions of the Asymmetric Exponentiated Bimodal Normal Model for Modeling Data with Positive Support

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  • Roger Tovar-Falón

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Guillermo Martínez-Flórez

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia
    These authors contributed equally to this work.)

  • Isaías Ceña-Tapia

    (Departamento de Matemáticas y Estadística, Facultad de Ciencias Básicas, Universidad de Córdoba, Montería 230002, Colombia)

Abstract

It is common in many fields of knowledge to assume that the data under study have a normal distribution, which often generates mistakes in the results, since this assumption does not always coincide with the characteristics of the observations under analysis. In some cases, the data may have degrees of skewness and/or kurtosis greater than what the normal model can capture, and in others, they may present two or more modes. In this work, two new families of skewed distributions are presented that fit bimodal data with positive support. The new families were obtained from the extension of the bimodal normal distribution to the alpha-power family class. The proposed distributions were studied for their main properties, such as their probability density function, cumulative distribution function, survival function, and hazard function. The parameter estimation process was performed from a classical perspective using the maximum likelihood method. The non-singularity of Fisher’s information was demonstrated, which made it possible to find the stochastic convergence of the vector of the maximum likelihood estimators and, based on the latter, perform statistical inference via the likelihood ratio. The applicability of the proposed distributions was exemplified using real data sets.

Suggested Citation

  • Roger Tovar-Falón & Guillermo Martínez-Flórez & Isaías Ceña-Tapia, 2023. "Some Extensions of the Asymmetric Exponentiated Bimodal Normal Model for Modeling Data with Positive Support," Mathematics, MDPI, vol. 11(7), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:7:p:1563-:d:1104877
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    References listed on IDEAS

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    1. Cavanaugh, Joseph E., 1997. "Unifying the derivations for the Akaike and corrected Akaike information criteria," Statistics & Probability Letters, Elsevier, vol. 33(2), pages 201-208, April.
    2. Heleno Bolfarine & Guillermo Martínez-Flórez & Hugo S. Salinas, 2018. "Bimodal symmetric-asymmetric power-normal families," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(2), pages 259-276, January.
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