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Title: A bimodal extension of the exponential distribution with applications in risk theory
Authors: Reyes, Jimmy
Gómez Déniz, Emilio 
Gómez, Héctor W.
Calderín Ojeda,Enrique 
UNESCO Clasification: 530202 Modelos econométricos
Keywords: Bimodal
Exponential distribution
Fit; life insurance
Issue Date: 2021
Project: Aportaciones A la Toma de Decisiones Bayesianas Óptimas: Aplicaciones Al Coste-Efectividad Con Datos Clínicos y Al Análisis de Riestos Con Datos Acturiales. 
Journal: Symmetry 
Abstract: There are some generalizations of the classical exponential distribution in the statistical literature that have proven to be helpful in numerous scenarios. Some of these distributions are the families of distributions that were proposed by Marshall and Olkin and Gupta. The disadvantage of these models is the impossibility of fitting data of a bimodal nature of incorporating covariates in the model in a simple way. Some empirical datasets with positive support, such as losses in insurance portfolios, show an excess of zero values and bimodality. For these cases, classical distributions, such as exponential, gamma, Weibull, or inverse Gaussian, to name a few, are unable to explain data of this nature. This paper attempts to fill this gap in the literature by introducing a family of distributions that can be unimodal or bimodal and nests the exponential distribution. Some of its more relevant properties, including moments, kurtosis, Fisher’s asymmetric coefficient, and several estimation methods, are illustrated. Different results that are related to finance and insurance, such as hazard rate function, limited expected value, and the integrated tail distribution, among other measures, are derived. Because of the simplicity of the mean of this distribution, a regression model is also derived. Finally, examples that are based on actuarial data are used to compare this new family with the exponential distribution.
ISSN: 2073-8994
DOI: 10.3390/sym13040679
Source: Symmetry [ISSN 2073-8994], v. 13(4), 679, (Abril 2021)
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