Exponentiated Extended Weibull-Power Series Class of Distributions

Tahmasebi, Saeid; Jafari, Ali Akbar

doi:10.5902/2179460x16680

Cited by 8 publications

(6 citation statements)

References 47 publications

(51 reference statements)

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“…The comparison is based on Cramer-von Mise (W), and Anderson-Darling (A) goodness-of-fit statistics. These two goodness-of-fit statistics are widely used to compare non-nested distributions and to determine how closely a specific cdf fits the empirical distribution of a given data set Tahmasebi and Jafari(2015). The lowest of these statistics indicate the model of best fit among the competing models Chen and Balakrishnan(1995).…”

Section: Applicationsmentioning

confidence: 99%

The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

Nwezza¹,

Ugwuowo²

2021

jas

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We introduce a new lifetime distribution called Marshall-Olkin extended Gumbel-Weibull. Some properties of distribution such as moments, TL-moments, quantile function, en- tropy, and order statistics are studied. The fexibility of the distribution to model unimodal, monotone shapes as well as unimodal, bimodal, monotone failure rates are presented. The estimators of the parameters of the distribution were obtained using the maximum likeli- hood estimation method. The performance of the maximum likelihood estimates of the Marshall-Olkin extended Gumbel-Weibulll parameters was observed through simulation studies. Two real life applications to illustrate the potentials of the new distribution are presented, and comparison with other distribution having the same baseline is done using goodness-of-test statistics.

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Section: Applicationsmentioning

confidence: 99%

The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

Nwezza¹,

Ugwuowo²

2021

jas

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“…The power series class can be used to construct many compounding models with discrete distributions: Poisson, logarithmic, geometric, binomial and negative-binomial. Some well-known compound models defined from the power series class are: Weibull power series (WPS) , complementary generalized-exponential power series (CGEPS) (Mahmoudi and Jafari 2012), complementary exponentiated-Weibull power series (CEWPS) (Mahmoudi and Shiran 2012b), extended WPS , Kumaraswamy power series (KwPS) (Bidram and Nekouhou 2013), complementary exponential power series (CEPS) (Flores et al 2013), Birnbaum-Saunders power series (BSPS) (Bourguignon et al 2014b), complementary WPS , complementary Erlang and Erlang power series (CErPS and ErPS) (Leahu et al 2014), complementary extended WPS , exponentiated extended WPS (Tahmasebi and Jafari 2015a), Burr XII power series (BIIPS) , Lindley power series (LPS) (Warahena-Liyanage and Pararai 2015a), linear failure rate power series (LFRPS) (Mahmoudi and Jafari 2015), complementary normal power series (CNPS) (Mahmoudi and Mahmoodian 2015), complementary generalized Gompertz power series (CGGoPS) (Tahmasebi and Jafari 2015b), complementary inverse Weibull power series (CIWPS) (Shafiei et al 2016), complementary generalized modified Weibull (CGMW) (Bagheri et al 2016), complementary exponentiated inverse Weibull power series (CEIWPS) (Hassan et al 2016), generalized gamma power series (GGPS) , Gompertz power series (GoPS) (Jafari and Tahmasebi 2016), complementary generalized linear failure rate power series (CGLFR) (Harandi and Alamatsaz 2016), and Dagum power series (DaPS) (Oluyede et al 2016b). …”

Section: Second Recent Trendmentioning

confidence: 99%

Compounding of distributions: a survey and new generalized classes

2016

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Generalizing distributions is an old practice and has ever been considered as precious as many other practical problems in statistics. It simply started with defining different mathematical functional forms, and then induction of location, scale or inequality parameters. The generalization through induction of shape parameter(s) started in 1997, and the last two decades were full of such practices. But to cope with the complex situations under series and parallel structures, the art of mixing discrete and continuous started in 1998. In this article, we present a survey on compounding univariate distributions, their extensions and classes. We review several available compound classes and propose some new ones. The recent trends in the construction of generalized and compounding classes are discussed, and the need for future works are addressed.

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“…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]).…”

Section: Introductionmentioning

confidence: 99%

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

Hassan

Almetwally

Gamoura

et al. 2022

Journal of Mathematics

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In this paper, we introduce the inverse exponentiated Lomax power series (IELoPS) class of distributions, obtained by compounding the inverse exponentiated Lomax and power series distributions. The IELoPS class contains some significant new flexible lifetime distributions that possess powerful physical explications applied in areas like industrial and biological studies. The IELoPS class comprises the inverse Lomax power series as a new subclass as well as several new flexible compounded lifetime distributions. For the proposed class, some characteristics and properties are derived such as hazard rate function, limiting behavior, quantile function, Lorenz and Bonferroni curves, mean residual life, mean inactivity time, and some measures of information. The methods of maximum likelihood and Bayesian estimations are used to estimate the model parameters of one optional model. The Bayesian estimators of parameters are discussed under squared error and linear exponential loss functions. The asymptotic confidence intervals, as well as Bayesian credible intervals, of parameters, are constructed. Simulations for a one-selective model, say inverse exponentiated Lomax Poisson (IELoP) distribution, are designed to assess and compare different estimates. Results of the study emphasized the merit of produced estimates. In addition, they appeared the superiority of Bayesian estimate under regarded priors compared to the corresponding maximum likelihood estimate. Finally, we examine medical and reliability data to demonstrate the applicability, flexibility, and usefulness of IELoP distribution. For the suggested two real data sets, the IELoP distribution fits better than Kumaraswamy–Weibull, Poisson–Lomax, Poisson inverse Lomax, Weibull–Lomax, Gumbel–Lomax, odd Burr–Weibull–Poisson, and power Lomax–Poisson distributions.

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Exponentiated Extended Weibull-Power Series Class of Distributions

Cited by 8 publications

References 47 publications

The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

The Marshall-Olkin Extended Gumbel-weibull Distribution: Properties And Applications

Compounding of distributions: a survey and new generalized classes

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

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