The exponentiated generalized power series

Abstract

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.

Inverse Exponentiated Lomax Power Series Distribution: Model, Estimation, and Application

“…Here, we obtain the expression for the incomplete moments of the IELoPS class. e r th incomplete moment of the IELoPS class, based on (16), is given by…”

“…In the last few decades, several papers have discussed the derivation of new probabilistic families by compounding different distributions with the PS model. Some notable compound classes proposed by several authors are as follows: exponential-PS family [1], Weibull-PS family [2], generalized exponential PS family [3], Burr XII-PS family [4], complementary Poisson Lindley-PS family [5], exponentiated extended Weibull family [6], complementary exponentiated inverted Weibull-PS family [7], Gompertz PS family [8], generalized modified Weibull-PS family [9], generalized inverse Weibull-PS family [10], exponential Pareto-PS family [11], exponentiated power Lindley-PS family [12], Burr-Weibull PS family [13], odd log-logistic PS family [14], generalized inverse Lindley PS family [15], exponentiated generalized PS family [16], exponentiated power generalized Weibull-PS family [17], new Lindley-Burr XII-PS [18], power function-PS family [19], inverse gamma PS family [20], and power quasi-Lindley PS family [21], among others. Recently, more generalized forms were provided by the compounding G-classes together with discrete distributions (see, for example, [22,23]).…”

The type II exponentiated half logistic-odd Burr X-G power series class of distributions with applications

“…Simultaneously, researchers have explored power series (PS) distributions as alternative for data fitting. They include the type II-EHL-Topp-Leone-G PS class of distributions (CoD) [24] , EHL- Topp-Leone-G PS CoD introduced [10] , exponentiated-G PS CoD introduced by [29] , odd power generalised Weibull-Weibull Poisson CoD [31] , odd Lindely-G PS CoD [8] , exponentiated half-logistic power generalized Weibull-G FoD [27] , exponentiated power Lindely Poisson distribution [33] , Ristic Balakrishnan Lindely Poisson distribution [14] , odd Weibull-Topp-Leone-G PS CoD [26] , Topp-Leone-G PS CoD [21] , Burr XII Weibull Logarithmic distribution [28] , generalized Burr XII PS CoD [13] , Lindely Burr XII PS CoD [20] , T-R Y PS CoD [32] , inverse Lindley PS CoD [35] and exponentiated extended Weibull PS CoD [38] , to mention just a few.…”