A new generalized Lindley-Weibull class of distributions: Theory, properties and applications

Abstract

We propose a new generalized class of distributions called Lindley-Weibull Power Series (LWPS) distributions and their special case called Lindley-Weibull logarithmic (LWL) distributions. Structural properties of the LWPS class of distributions and its sub-model LWL distribution including moments, order statistics, Rényi entropy, mean and median deviations, Bonferroni and Lorenz curves, and maximum likelihood estimates are derived. A simulation study to examine the bias and mean square error of the maximum likelihood estimators for each parameter is presented. Finally, real data examples are presented to illustrate the applicability and usefulness of the proposed class of distributions.

A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application

“…Various compound classes have been provided by mixing continuous distributions with power series (PS) distribution, for example, Weibull-PS and extended Weibull-PS (Morais and Barreto-Souza [2] and Silva et al [3]), generalized exponential PS (Mahmoudi and Jafari [4]), complementary exponential PS (Flores et al [5]), the Burr XII-PS (Silva and Corderio [6]), Gompertz PS (Jafari and Tahmasebi [7]), generalized modifed Weibull-PS (Bagheri et al [8]), exponential Pareto PS (Elbatal et al [9]), exponentiated power Lindley-PS (Alizadeh et al [10]), generalized inverse Lindley-PS (Alkarni, [11]), Burr-Weibull PS (Oluyede et al [12]), odd log-logistic PS (Goldoust et al [13]), new generalized Lindley-Weibull class (Makubate et al [14]), inverse gamma PS (Rivera et al [15]), and inverted exponentiated Lomax PS (Hassan et al [16]) among others.…”

The odd power generalized Weibull-G power series class of distributions: properties and applications

“…Several generalized distributions proposed in the literature involving the power series include the exponentiated generalized power series class of distributions by Oluyede et al (2020c), a new generalized Lindley-Weibull class of distributions by Makubate et al (2020), the exponentiated power generalized Weibull power series family of distributions by Aldahlan et al (2019), Weibull-power series distributions by Morais and Barreto-Souza (2011), complementary exponential power series by Flores et al (2013), complementary extended Weibull-power series by Cordeiro and Silva (2014), Burr XII power series by Silva and Silva and Cordeiro (2015), extended Weibull-power series (EWPS) distribution by Silva et al (2013).…”

Type II Exponentiated Half-Logistic-Topp-Leone-G Power Series Class of Distributions with Applications

“…The power series family of distributions include binomial, Poisson, geometric and logarithmic distributions Johnson et al (14). Several generalized distributions proposed in the literature involving the power series include the exponentiated power generalized Weibull power series family of distributions by Aldahlan et al ( 2), the T-R {Y } power series family of probability distributions by Osatohanmwen et al (25), exponentiated generalized power series class of distributions by Oluyede et al (22), a new generalized Lindley-Weibull class of distributions by Makubate et al (17), the odd Weibull-Topp-Leone-G power series family of distributions by Oluyede et al (21), Weibull-power series distributions by Morais and Barreto-Souza (18), complementary exponential power series by Flores et al (11), complementary extended Weibullpower series by Cordeiro and Silva (9), Burr XII power series by Silva and Cordeiro (31), extended Weibull-power series (EWPS) distribution by Silva et al (30) and the Burr-Weibull power series class of distributions by Oluyede et al (23).…”