Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA; Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana; Corresponding author at: Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana.
B. Mashabe
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
A. Fagbamigbe
Department of Epidemiology and Medical Statistics, College of Medicine, University of Ibadan, Nigeria
B. Makubate
Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Palapye, Botswana
D. Wanduku
Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA, 30460, USA
We propose a new generalized family of distributions called the exponentiated generalized power series (EGPS) family of distributions and study its sub-model, the exponentiated generalized logarithmic (EGL) class of distributions, in detail. The structural properties of the new model (EGPS) and its sub-model (EGL) distribution including moments, order statistics, Rényi entropy, and maximum likelihood estimates are derived. We used the method of maximum likelihood to estimate the parameters of this new family of distributions. Simulation study was carried out to examine the bias and the mean square error of the maximum likelihood estimators for each of the model's parameters. Finally, we showed real life data examples to illustrate the models' applicability, flexibility and usefulness.
