Gompertz-power series distributions

Abstract

In this paper, we introduce the Gompertz power series (GPS) class of distributions which is obtained by compounding Gompertz and power series distributions. This distribution contains several lifetime models such as Gompertz-geometric (GG), Gompertz-Poisson (GP), Gompertz-binomial (GB), and Gompertz-logarithmic (GL) distributions as special cases. Sub-models of the GPS distribution are studied in details. The hazard rate function of the GPS distribution can be increasing, decreasing, and bathtub-shaped. We obtain several properties of the GPS distribution such as its probability density function, and failure rate function, Shannon entropy, mean residual life function, quantiles and moments. The maximum likelihood estimation procedure via a EM-algorithm is presented, and simulation studies are performed for evaluation of this estimation for complete data, and the MLE of parameters for censored data. At the end, a real example is given.

Generating New Flexible Lifetime Class of Distributions Based on Competing Risks and Frailty Models

“…The following scenarios of the parameter vector θ = (a, b, θ, p) are considered: (0.2, 2.5, 0.25, 1.7), (1.6, 0.9, 1.4, 0.8) and (5,8,5,7). These selected values of θ gives unimodal, decreasing and decreasing-increasing-decreasing shapes for pdf of the EGG distribution.…”

“…Jafari et al [5] proposed beta Gompertz (BG) distribution using beta generator introduced by Eugene et al [6]. Gompertz power series distributions by Jafri and Tahmasebi [7], using the technique of Marshall and Olkin [8]. Transimuted Gompertz (TG) distribution by Abdul-Moniem and Seham [9], who considered transmuted generator introduced by Show and Buckley [10].…”

A New Extension of the Generalized Half Logistic Distribution with Applications to Real Data

“…Proposition 6. Let X be a random variable with pdf in (5), If Y = 1 γ log γ log 1+e −αx 2e −αx + θ /θ , then Y has the Poisson generalized Gompertz (PGG) with parameters a, θ, γ, λ > 0, mention in [11] and if a = 1 we have Gompertz Poisson (GP) [29]. therefore,…”

“…Next, we can compared PoiGHL with its sub model by conducting a likelihood ratio test (LR). Let considerθ andθ be the unrestricted and restricted MLEs of θ respectively, then the LR test between the null hypothesis H 0 : θ 1 = θ 0 1 versus alternative hypothesis H 1 : Now, we study the existence and uniqueness of the MLEs as discussed in [29,34,35] among others.…”

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). …”