A new generalized Weibull family of distributions: mathematical properties and applications

We propose a generalized Weibull family of distributions with two extra positive parameters to extend the normal, gamma, Gumbel and inverse Gausssian distributions, among several other well-known distributions. We provide a comprehensive treatment of its general mathematical properties including quantile and generating functions, ordinary and incomplete moments and other properties. We introduce the log-generalized Weibull-log-logistic, this is new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data.

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