We propose a new family of continuous distributions called the odd generalized exponential family, whose hazard rate could be increasing, decreasing, J, reversed-J, bathtub and upside-down bathtub. It includes as a special case the widely known exponentiated-Weibull distribution. We present and discuss three special models in the family. Its density function can be expressed as a mixture of exponentiated densities based on the same baseline distribution. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics. For the first time, we obtain the generating function of the Fréchet distribution. Two useful characterizations of the family are also proposed. The parameters of the new family are estimated by the method of maximum likelihood. Its usefulness is illustrated by means of two real lifetime data sets.

We propose a new class of continuous distributions with two extra shape parameters named the generalized odd log-logistic family of distributions. The proposed family contains as special cases the proportional reversed hazard rate and odd log-logistic classes. Its density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. Some of its mathematical properties including ordinary moments, quantile and generating functions, two entropy measures and order statistics are obtained. We derive a power series for the quantile function. We discuss the method of maximum likelihood to estimate the model parameters. We study the behaviour of the estimators by means of Monte Carlo simulations. We introduce the log-odd log-logistic Weibull regression model with censored data based on the odd log-logistic-Weibull distribution. The importance of the new family is illustrated using three real data sets. These applications indicate that this family can provide better fits than other well-known classes of distributions. The beauty and importance of the proposed family lies in its ability to model different types of real data.

We study some mathematical properties of a new generator of continuous distributions with two extra parameters called the exponentiated half-logistic family. We present some special models. We investigate the shapes of the density and hazard rate function. We derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, and order statistics, which hold for any baseline model. We introduce two bivariate extensions of this family. We discuss the estimation of the model parameters by maximum likelihood and demonstrate the potentiality of the new family by means of two real data sets.

We introduce and study some general mathematical properties of a new generator of continuous distributions with two extra parameters called the Gompertz-G generator. We present some special models. We investigate the shapes of the density and hazard functions and derive explicit expressions for the ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Bonferroni and Lorenz curves, Shannon and Rényi entropies, and order statistics. Two bivariate extensions of this model are proposed. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the potentiality of the new class by means of two real data sets.

We study general mathematical properties of a new class of continuous distributions with an extra positive parameter called the type I half-logistic family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. Explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order statistics are determined. We introduce a bivariate extension of the new family. We discuss the estimation of the model parameters by maximum likelihood and illustrate its potentiality by means of two applications to real data.

We introduce a new family of continuous distributions called the Kumaraswamy Marshal-Olkin generalized family of distributions. We study some mathematical properties of this family. Its density function is symmetrical, left-skewed, right-skewed and reversed-J shaped, and has constant, increasing, decreasing, upside-down bathtub, bathtub and S-shaped hazard rate. We present some special models and investigate the asymptotics and shapes of the family. We derive a power series for the quantile function and obtain explicit expressions for the moments, generating function, mean deviations, two types of entropies and order statistics. Some useful characterizations of the family are also proposed. The method of maximum likelihood is used to estimate the model parameters. We illustrate the importance of the family by means of two applications to real data sets