Journal of Data Science

In this paper, we introduce some new families of generalized Pareto distributions using the T-R{Y} framework. These families of distributions are named T-Pareto{Y} families, and they arise from the quantile functions of exponential, log-logistic, logistic, extreme value, Cauchy and Weibull distributions. The shapes of these T-Pareto families can be unimodal or bimodal, skewed to the left or skewed to the right with heavy tail. Some general properties of the T-Pareto{Y} family are investigated and these include the moments, modes, mean deviations from the mean and from the median, and Shannon entropy. Several new generalized Pareto distributions are also discussed. Four real data sets from engineering, biomedical and social science are analyzed to demonstrate the flexibility and usefulness of the T-Pareto{Y} families of distributions.

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.