Characterizations of a New Generalized Family of Distributions

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Abstract This paper introduces a new family that extends some lifetime distributions, such as the Weibull, inverse Weibull, Lomax, logistic, and log-logistic distributions, which could be applied in several fields, especially to fit lifetime data. This family has a monotonically increasing and decreasing hazard rate. Some characteristics of one of these distributions, such as the Weibull-Logistic distribution, have been studied, including the hazard rate function, quantile function, moments, and distribution of the order statistics. Three real data sets have been studied that show this distribution can be used quite effectively in fitting and analyzing real lifetime data and provides a better fit than other well-known lifetime models such as Weibull, inverse Weibull, and log-logistic distributions. Finally, Monte Carlo simulations have been carried out to calculate the asymptotic confidence bounds for the distribution parameters.

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