Topp-Leone Gompertz Distribution: Properties and Applications

Abstract

This paper proposes the Topp-Leone Gompertz distribution; an extension of the Gompertz distribution for modeling real life time data. The new model is obtained by transforming the cumulative distribution function of the Gompertz random variable, while taking the Topp-Leone as the generator. Some statistical properties of the new distribution are derived. Maximum likelihood estimates of model parameters are also derived. A Monte Carlo simulation study is carried out to examine the accuracy of the maximum likelihood estimate of the distribution parameters. Two real data sets are used to illustrate the applicability of the new distribution, and the results show that the new distribution outperforms some related lifetime distributions.

The alpha power Teissier distribution and its applications

“…Figure 2 shows the empirical densities, and cdf s with the Stress-rupture life data set for some models. The second data as used in Afify et al(2016), Eghwerido et al(2019), Eghwerido et al(2020), Nzei et al(2020), Eghwerido et al(2021a), Eghwerido et al(2021b), Eghwerido et al(2021) andZelibe et al(2019) consist of 63 workers at the UK National Physical Laboratory observations of strength of 1.5cm glass fibers in Korkmaz et al(2018), Eghwerido and Agu(2021c) and Smith and Naylor(1987). The results of the test statistics are shown in Table 3.…”

“…Hence, several classical distributions have been modified using the alpha power characterization of Mahdavi and Kundu(2017). For examples, the alpha power Gompertz by Eghwerido et al(2021), Marshall-Olkin Sujatha distribution by Agu and Eghwerido(2021b), alpha power Weibull Frechet by Burton et al(2020), the alpha power inverted exponential by Unal et al(2018), exponentiated Teissier distribution by Sharma et al(2020), Weibull alpha power inverted exponential distribution by Eghwerido et al(2020), alpha power Marshall-Olkin-G by Eghwerido et al(2021b), transmuted alpha power-G by Eghwerido et al(2020b), Gompertz alpha power inverted exponential by Eghwerido et al(2020a), Kumaraswamy Alpha power inverted exponential distribution by Zelibe et al(2019), alpha power Weibull distribution by Nassar et al(2017), alpha power transformed generalized exponential distribution by Nadarajah and Okorie(2017), alpha power shifted exponential by Eghwerido et al(2021d), Marshall-Olkin alpha power family of distributions by Nassar et al(2017a), Topp-Leone Gompertz distribution by Nzei et al(2020), Weibull Frechet distribution by Afify et al(2016), Type 11 Topp-Leone Generalized Power Ishita distribution by Agu et al(2020c), Inverse odd Weibull generated family of distributions by Eghwerido et al(2020c), Zubair Gompertz distribution by Eghwerido et al(2021a), Gompertz extended generalized exponential distribution by Eghwerido et al(2020d), quasi Xgamma-Poisson distribution by Sen et al(2019), Agu-E Distribution by Burton et al(1986), and a two parameter exponential distribution based on progressive type II censored data by Belaghi et al(2015).…”

The Marshall-Olkin-Topp-Leone-Gompertz-G Family of Distributions with Applications

“…The importance of generalizing those distributions is that they provide a better fit than the existing ones in modeling real-life data. Some examples of those generalized distributions include, the Marshall-Olkin-Gompertz-G family of distributions by Chipepa and Oluyede [12], the Marshall-Olkin extended generalized Gompertz distribution by Lazhar [23], Topp-Leone Gompertz distribution by Nzei et al [29] and the Gompertz-G family of distributions by Alizadeh et al [2]. Some Topp-Leone generalizations in the literature including the Marshall-Olkin Topp-Leone half-logistic-G family of distributions by Sengweni et al [33], Topp-Leone odd Burr III-G family of distributions by Moakofi et al [28] and Topp-Leone odd Burr X-G Family of distributions by Oluyede et al [31].…”

The Topp-Leone-Gompertz-Exponentiated Half Logistic-G Family of Distributions with Applications

“…We take λ = 1, in this paper to avoid the problem of overparameterization. Jafari et al (2014) developed the beta-Gompertz distribution, Roozegar et al (2017) considered the properties and applications of McDonald-Gompertz distribution, Nzei et al (2020) introduced Topp-Leone-Gompertz distribution, Eghwerido et al (2021) proposed the alpha power Gompertz distribution, Lenart & Missov (2016) considered goodness-of-fit statistics for the Gompertz distribution, El-Bassiouny et al (2017) proposed exponentiated generalized Weibull-Gompertz distribution, Khaleel et al (2020) introduced Marshall-Olkin exponential Gompertz distribution, Benkhelifa (2017) presented the Marshall-Olkin extended generalized Gompertz distribution, Elbatal et al (2018) proposed the modified beta Gompertz distribution, Shama et al (2022) developed the gammaGompertz distribution, Boshi et al (2020) proposed the generalized gammageneralized Gompertz distribution, El-Morshedy et al (2020) proposed Kumaraswamy inverse Gompertz distribution, and De Andrade et al (2019) introduced the exponentiated generalized extended Gompertz distribution. Some recent generalizations of the exponentiated half logistic distribution include: exponentiated half logistic-odd Burr III-G family of distributions by Oluyede, Peter, Ndwapi & Bindele (2022), exponentiated half logistic-power generalized Weibull-G family of distributions by Oluyede et al (2021), type II exponentiated half logistic-Topp-Leone-Marshall-Olkin-G family of distributions by Moakofi et al (2021), exponentiated half logistic-odd Lindley-G family of distributions by Sengweni et al (2021), exponentiated half logistic-odd Weibull-Topp-Leone-G family of distributions by , and exponentiated half logistic-log-logistic Weibull distribution by Chamunorwa et al (2021).…”