Journal of Data Science

In this paper, we introduce a new lifetime model, called the Gen- eralized Weibull-Burr XII distribution. We discuss some of its mathematical properties such as density, hazard rate functions, quantile function and mo- ments. Maximum likelihood method is used to estimate model parameters. A simulation study is performed to assess the performance of maximum like- lihood estimators by means of biases, mean squared errors. Finally, we prove that the proposed distribution is a very competitive model to other classical models by means of application on real data set.

We introduce a four-parameter distribution, called the Zografos-Balakrishnan Burr XII distribution. Our purpose is to provide a Burr XII generalization that may be useful to still more complex situations. The new distribution may be an interesting alternative to describe income distributions and can also be applied in actuarial science, finance, bioscience, telecommunications and modelling lifetime data, for example. It contains as special models some well-known distributions, such as the log-logistic, Weibull, Lomax and Burr XII distributions, among others. Some of its structural properties are investigated. The method of maximum likelihood is used for estimating the model parameters and a simulation study is conducted. We provide two application to real data to demonstrate the usefulness of the proposed distribution. Since the Risti´c-Balakrishnan Burr XII distribution has a similar structure to the studied distribution, we also present some of its properties and expansions.

ABSTRACT：A new distribution called the exponentiated Burr XII Weibull(EBW) distributions is proposed and presented. This distribution contains several new and known distributions such as exponentiated log-logistic Weibull, exponentiated log-logistic Rayleigh, exponentiated log-logistic exponential, exponentiated Lomax Weibull, exponentiated Lomax Rayleigh, exponentiated Lomax Exponential, Lomax Weibull, Lomax Rayleigh Lomax exponential, Weibull, Rayleigh, exponential and log-logistic distributions as special cases. A comprehensive investigation of the properties of this generalized distribution including series expansion of probability density function and cumulative distribution function, hazard and reverse hazard functions, quantile function, moments, conditional moments, mean deviations, Bonferroni and Lorenz curves, R´enyi entropy and distribution of order statistics are presented. Parameters of the model are estimated using maximum likelihood estimation technique and real data sets are used to illustrate the usefulness and applicability of the new generalized distribution compared with other distributions.