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Likelihood-Based Inference for the Asymmetric Exponentiated Bimodal Normal Model
Inferencia basada en verosimilitud para el modelo asimétrico bimodal normal exponenciado
DOI:
https://doi.org/10.15446/rce.v45n2.95530Keywords:
Alpha-Power distribution, Asymmetric models, Bimodal normal distribution, Censored data, Maximum likelihood estimation (en)Distribución normal bimodal, Distribución alfa-potencia, Datos censurados, Modelos asimétricos, Estimación por máxima verosimilitud (es)
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Asymmetric probability distributions have been widely studied by various authors in recent decades, who have introduced new families of flexible distributions in terms of skewness and kurtosis than the classical distributions known in statistical theory. Most of the new distributions fit unimodal data, others fit bimodal data, however, in the bimodal, singularity problems have been found in their information matrices in most of the proposals presented. In contrast, in this paper an extension of the family of alpha-power distributions was developed, which has a non-singular information matrix, based on the bimodal-normal and bimodal elliptic-skew-normal probability distributions. These new extensions model asymmetric bimodal data commonly found in various areas of scientific interest. The properties of these new probabilistic distributions were also studied in detail and the respective statistical inference process was carried out to estimate the parameters of these new models. The stochastic convergence for the vector of maximum likelihood estimators could be found due to the non-singularity of the expected information matrix in the corresponding support.
Las distribuciones de probabilidad asimétricas han sido ampliamente estudiadas por varios autores en las últimas décadas, quienes han introducido nuevas familias de distribuciones flexibles en términos de asimetría y curtosis que las distribuciones clásicas conocidas en teoría estadística. La mayoría de las nuevas distribuciones se ajustan a datos unimodales, otras se ajustan a datos bimodales, sin embargo, en el caso bimodal, se han encontrado problemas de singularidad en la matriz de información en la mayoría de las propuestas presentadas. En contraste, en este trabajo se desarrolló una extensión de la familia de distribuciones de alfa-potencia, la cual tiene una matriz de información no singular, basada en las distribuciones de probabilidad normal-bimodal y bimodal elíptica-sesgada-normal. Estas nuevas extensiones modelan datos bimodales asimétricos que se encuentran comúnmente en diversas áreas de interés científico. También se estudiaron en detalle las propiedades de estas nuevas distribuciones probabilísticas y se llevó a cabo el respectivo proceso de inferencia estadística para estimar los parámetros de estos nuevos modelos. La convergencia estocástica para el vector de estimadores de máxima verosimilitud se pudo encontrar debido a la no singularidad de la matriz de información esperada en el soporte correspondiente.
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1. Fernando Arturo Peña Ramírez, Renata Guerra, Gauss Cordeiro . (2023). A New Nadarajah-Haghighi Generalization with Five Different Shapes for the Hazard Function. Revista Colombiana de Estadística, 46(2), p.93. https://doi.org/10.15446/rce.v46n2.103412.
2. 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, 11(7), p.1563. https://doi.org/10.3390/math11071563.
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