The compound class of linear failure rate-power series distributions: Model, properties, and applications

Abstract

We introduce in this paper a new class of distributions which generalizes the linear failure rate (LFR) distribution and is obtained by compounding the LFR distribution and power series (PS) class of distributions. This new class of distributions is called the linear failure rate-power series (LFRPS) distributions and contains some new distributions such as linear failure rate geometric (LFRG) distribution, linear failure rate Poisson (LFRP) distribution, linear failure rate logarithmic (LFRL) distribution, linear failure rate binomial (LFRB) distribution and Raylight-power series (RPS) class of distributions. Some former works such as exponential-power series (EPS) class of distributions, exponential geometric (EG) distribution, exponential Poisson (EP) distribution and exponential logarithmic (EL) distribution are special cases of the new proposed model.The ability of the LFRPS class of distributions is in covering five possible hazard rate function i.e., increasing, decreasing, upside-down bathtub (unimodal), bathtub and increasing-decreasing-increasing shaped. Several properties of the LFRPS distributions such as moments, maximum likelihood estimation procedure via an EM-algorithm and inference for a large sample, are discussed in this paper. In order to show the flexibility and potentiality of the new class of distributions, the fitted results of the new class of distributions and some its submodels are compared using a real data set.

Compounding of distributions: a survey and new generalized classes

“…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). …”

Exponentiated Extended Weibull-Power Series Class of Distributions

“…If b = 0, it becomes to GEPS class of distributions. Also, If β = 1, it becomes to linear failure rate-power series introduced by Mahmoudi and Jafari (2014).…”

“…We call it exponentiated extended Weibull-power series (EEWPS) class of distributions. In similar way, some distributions are proposed in literature: the exponential-power series (EP) distribution by Chahkandi and Ganjali (2009), Weibull-power series (WPS) distributions by Morais and Barreto-Souza (2011), generalized exponential-power series (GEP) distribution by Mahmoudi and Jafari (2012), complementary exponential power series by Flores et al (2013), extended Weibull-power series (EWPS) distribution by , double bounded Kumaraswamypower series by Bidram and Nekoukhou (2013), Burrpower series by , generalized linear failure rate-power series (GLFRP) distribution by Alamatsaz and Shams (2014), Birnbaum-Saunderspower series distribution by Bourguignon et al (2014), linear failure rate-power series by Mahmoudi and Jafari (2014), and complementary extended Weibull-power series by Cordeiro and Silva (2014). Similar procedures are used by Roman et al (2012), Lu andShi (2011), Nadarajah et al (2015) and Louzada et al (2014).…”

A new four-parameter lifetime distribution

“…Adamidis and Loukas (1998) pioneered a two-parameter exponential-geometric (EG) distribution by compounding the exponential and geometric distributions. In a similar manner, the following distributions were proposed: exponential-logarithmic (EL) distribution (Tahmasbi and Rezaei, 2008); exponential-power series (EPS) distribution (Chahkandi and Ganjali, 2009 (Tojeiro et al, 2014); Burr XII negative binomial distribution (Ramos, 2015); compound class of extended Weibull power series distributions (Silva, 2013); compound class of linear failure rate-power series distributions (Mahmoudi and Jafari, 2014); exponentiated Weibull-logarithmic distribution (Mahmoudi and Sepahdar, 2013); exponentiated Weibull-logarithmic distribution ; generalized exponential power series distribution (Mahmoudi and Jafari, 2012); exponentiated Weibull power series distribution (Mahmoudi and Shiran, 2012); generalized modified Weibull power series distribution (Bagheri et al, 2015). Lindley (1958) introduced a one-parameter distribution, known as Lindley distribution, given by its probability density function (pdf) The aim of this paper is to propose a new class of lifetime distributions called the exponentiated power Lindley geometric (EPLG) distribution.…”