Parameter estimation of an extended inverse power Lomax distribution with Type I right censored data

Abstract

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four-parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

Different estimation methods for the unit inverse exponentiated weibull distribution

“…Inverted distributions have a different structure than non-inverted distributions in terms of density and hazard rate shapes. Several writers have dedicated a great deal of time and effort to discuss inverted distributions and their applications; such as, the inverse weibull distribution (Keller and Kamath, 1982), the inverted Lindley distribution (Sharma et al, 2015), the inverted power Lindley distribution (Barco et al, 2017), the inverted Kumaraswamy distribution (Abd AL-Fattah et al, 2017), inverted exponentiated weibull distribution (Lee et al, 2017), inverted Nadarajah-Haghighi distribution (Tahir et al, 2018), inverse power Lomax distribution (Hassan and Abd-Allah, 2019), inverse exponentiated Lomax distribution (Hassan and Mohamed, 2019), and inverted Topp-Leone distribution (Hassan et al, 2020 among others.…”

A New Power Topp–Leone distribution with applications to engineering and industry data

“…This modification is a novelty in the literature. The following are some prominent instances of such families: Poisson-G [ 1 ], Odd Fréchet-G [ 2 ], Truncated inverse Kumaraswamy-G [ 3 ], New Power of Topp-Leone-G [ 4 ], Introduction to the generalized Topp-Leone family [ 5 ], Garhy-G [ 6 ], Inverse-Lomax power [ 7 ], Half-Logistic-G type II [ 8 ], Topp-Leone Inverse Lomax [ 9 ], Topp-Leone-Weibull [ 10 ], temporal distribution [ 11 ], Topp-Leone distribution, estimation [ 12 ], Topp-Leone family of distributions and some of its application on real data and some of its statsistical properties [ 13 ], moments of order statistics of Topp-Leone distribution [ 14 ] Fréchet Topp-Leone-G [ 15 ], Topp-Leone G transmuted [ 16 ], new insights on goodness-of-fit tests [ 17 ], a generalized Birnbaum-Saunders distribution [ 18 ], efficient reliability estimation in two-parameter exponential distributions [ 19 ], the Marshall-Olkin extended generalized Rayleigh distribution [ 20 ], tests to determine whether or not the Rayleigh distribution is a good fit [ 21 ], Bayesian analysis [ 22 , 23 ] is also of big interest in our study.…”

Classical and Bayesian estimation for Gompertz distribution under the unified hybrid censored sampling with application

“…This plan has previously been covered in several literary works, see, for example, those by Balakrishnan and Kundu, 3 Huang and Yang, 4 Habibi Rad and Izanlo, 5 Panahi and Sayyareh, 6 Jeon and Kang, 7 Sarkar and Tripathy, 8 and Dutta et al 9 Recently, many researchers have been interested in using different types of schemes using many lifetime models through many applications. For more details, see the works by Nassar et al, 10 Nassr and Elharoun, 11 Hassan et al, 12 Nassr and Azm, 13 El Azm et al, 14 Yousef et al, 15 Elgarhy et al, 16,17 Bantan et al, 18,19 Elbatal et al, 20 Shrahili et al, 21 Algarni et al, 22 Alotaibi et al, 23 Ahmadini et al, 24 Mohamed et al, 25 Abdelwahab et al, 26 Alyami et al, 27 Helmy et al, 28 Hassan and Nassr, 29,30 and Abd-Elfattah et al 31 The Gompertz distribution, first proposed by Benjamin Gompertz as a model for the distribution of income in Ref. 32, is considered to represent the underlying distribution in this study.…”