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: We propose a new method of adding two parameters to a contin uous distribution that extends the idea first introduced by Lehmann (1953) and studied by Nadarajah and Kotz (2006). This method leads to a new class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann alternatives. Some special models are dis cussed. We derive some mathematical properties of this class including the ordinary moments, generating function, mean deviations and order statis tics. Maximum likelihood estimation is investigated and four applications to real data are presented.