A new Lindley-Burr XII power series distribution: model, properties and applications

Abstract

A new generalized class of distributions called the Lindley-Burr XII Power Series (LBXIIPS) distribution is proposed and explored. This new class of distributions contain some special cases such as Lindley-Burr XII Poisson (LBXIIP), Lindley-Burr XII Logarithmic (LBXIIL), Lindley-Burr XII Binomial (LBXIIB) and their sub-models among others. Some structural properties of the new distribution including moments, probability weighted moments, distribution of the order statistics and entropy are derived. Maximum likelihood estimation technique is used to estimate the model parameters. A simulation study to examine the bias and mean square error of the maximum likelihood estimators is presented and finally, an application to a real data set in order to illustrate the usefulness of the new distribution is given.

New Weighted Burr XII Distribution: Statistical Properties, Applications, and Regression

“…Te precipitation (in inches) in the Minneapolis dataset was used in [30,31]. Te second dataset represents runof amounts at Jug Bridge, Maryland, and was used by Makubate et al [32]. Te performance of the MAPTBXII distribution is compared with the Topp-Leone Burr-XII distribution (TLBXII) [33], Weibull Burr XII distribution (WBXII) [29], inverse Weibull distribution (INW) [34], exponentiated exponential Burr XII distribution (EEBXII) [35], Cauchy [36], and inverse Gompertz distribution (IGD) [37].…”

On the Extension of the Burr XII Distribution: Applications and Regression

“…Several works in the literature have been done to improve the flexibility of the Burr XII distribution. The Marshall-Olkin exponentiated Burr XII distribution [2], the Marshall-Olkin Generalised Burr XII distribution [3], the Lindley-Burr XII distribution [4], the Kumaraswamy exponentiated Burr XII distribution [5], the Weibull Burr XII distribution [6], the Kumaraswamy Burr XII distribution [7], order statistics of inverse Pareto distribution [8], the exponentiated exponential Burr XII distribution [10], the Garhy-Burr XII [11], the equilibrium renewal Burr XII distribution [12], the Gompertz-modified Burr XII distribution [13], and the odd exponentiated half-logistic Burr XII distribution [14].…”

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.…”