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.

In this paper, we define and study a four-parameter model called the transmuted Burr XII distribution. We obtain some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, order statistics, probability weighted moments and entropies. We formulate and develop a log-linear model using the new distribution so-called the log-transmuted Burr XII distribution for modeling data with a unimodal failure rate function, as an alternative to the log-McDonald Burr XII, log-beta Burr XII, log-Kumaraswamy Burr XII, log-Burr XII and logistic regression models. The flexibility of the proposed models is illustrated by means of three applications to real data sets.

We introduce the four-parameter Kumaraswamy Gompertz distribution. We obtain the moments, generating and quantilefunctions, Shannon and Rényi entropies, mean deviations and Bonferroni and Lorenz curves. We provide a mixture representation for the density function of the order statistics. We discuss the estimation of the model parameters by maximum likelihood. We provide an application a real data set that illustrates the usefulness of the new model.

In this paper, we considered a new generalization of the paralogistic distribution which we called the three-parameter paralogistic distribution. Some properties of the new distribution which includes the survival function, hazard function, quantile function, moments, Renyi entropy and the maximum likelihood estimation (MLE) of its parameters are obtained. A simulation study shows that the MLE of the parameters of the new distribution is consistent and asymptotically unbiased. An applicability of the new three-parameter paralogistic distribution was subject to a real lifetime data set alongside with some related existing distributions such as the Paralogistic, Gamma, Transformed Beta, Log-logistic and Inverse paralogistic distributions. The results obtained show that the new three-parameter paralogistic distribution was superior to other aforementioned distributions in terms of the Akaike information criterion (AIC) and K-S Statistic values. This claim was further supported by investigating the density plots, P-P plots and Q-Q plots of the distributions for the data set under study.

The so-called Kumaraswamy distribution is a special probability distribution developed to model doubled bounded random processes for which the mode do not necessarily have to be within the bounds. In this article, a generalization of the Kumaraswamy distribution called the T-Kumaraswamy family is defined using the T-R {Y} family of distributions framework. The resulting T-Kumaraswamy family is obtained using the quantile functions of some standardized distributions. Some general mathematical properties of the new family are studied. Five new generalized Kumaraswamy distributions are proposed using the T-Kumaraswamy method. Real data sets are further used to test the applicability of the new family.