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The Zografos-Balakrishnan Type-I Heavy-Tailed-G Family of Distributions with Applications
La familia de distribuciones Zografos-Balakrishnan tipo I de colas pesadas G con aplicaciones
DOI:
https://doi.org/10.15446/rce.v47n2.111985Keywords:
Zografos-Balakrishnan, Baseline Distribution, Heavy-Tailed, Actuarial Measures, Estimation, Simulations (en)Distribución de referencia, Cola pesada, Estimación, Medidas actuariales, Simulaciones, Zografos-Balakrishnan. (es)
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We propose a new family of distributions called the Zografos-Balakrishnan type-I heavy-tailed-G (ZBTIHT-G) distributions. A special model of the proposed family, namely Zografos-Balakrishnan type-I heavy-tailed-Weibull (ZBTIHT-W) model is thoroughly studied. Statistical properties of the new family of distributions including, among others, the hazard rate function, quantile function, moments, distribution of order statistics and Rényi entropy are presented. The maximum likelihood method of estimation is used for estimating the model parameters and Monte Carlo simulation is conducted to examine the performance of the estimators of the model parameters.The flexibility and importance of the new family of distributions are demonstrated by means of applications to real data sets.
Proponemos una nueva familia de distribuciones Zografos-Balakrishnan tipo I de colas pesadas G con aplicaciones (ZBTIHT-G). Un modelo especial de la familia propuesta Zografos-Balakrishnan tipo I-Weibull de cola pesada (ZBTIHT-W) está profundamente estudiada. Propiedades estadísticas de la nueva familia de distribuciones que incluyen, entre otras, la función de tasa de riesgo. Se presenta la función cuantil, momentos, distribución de esta dísticas de orden y entropía de Rényi. Se utiliza el método de estimación de máxima verosimilitud para estimar los parámetros del modelo y se realiza una simulación de Monte Carlo para examinar el desempeño de los estimadores de los parámetros del modelo. La flexibilidad e importancia de la nueva familia de distribuciones son demostradas mediante aplicaciones a conjuntos de datos reales.
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