A New Asymmetric Modified Topp–Leone Distribution: Classical and Bayesian Estimations under Progressive Type-II Censored Data with Applications

Abstract

In this article, a new modified asymmetric Topp–Leone distribution is created and developed from a theoretical and inferential point of view. It has the feature of extending the remarkable flexibility of a special one-shape-parameter lifetime distribution, known as the inverse Topp–Leone distribution, to the bounded interval [0, 1]. The probability density function of the proposed truncated distribution has the potential to be unimodal and right-skewed, with different levels of asymmetry. On the other hand, its hazard rate function can be increasingly shaped. Some important statistical properties are examined, including several different measures. In practice, the estimation of the model parameters under progressive type-II censoring is considered. To achieve this aim, the maximum likelihood, maximum product of spacings, and Bayesian approaches are used. The Markov chain Monte Carlo approach is employed to produce the Bayesian estimates under the squared error and linear exponential loss functions. Some simulation studies to evaluate these approaches are discussed. Two applications based on real-world datasets—one on the times of infection, and the second dataset is on trading economics credit rating—are considered. Thanks to its flexible asymmetric features, the new model is preferable to some known comparable models.

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

“…The whole conditional posterior PDF of the parameters α, λ cannot be reduced to a well-known distribution, as shown by (17). As a result, we consider the Metropolis-Hastings algorithm, one of the MCMC techniques, to generate posterior samples of the parameters α, λ from the full conditional posterior PDF to calculate the Bayesian estimates of the unknown parameters α, λ, the reliability R(t), and the hazard rate H(t) functions.…”

“…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.…”

Reliability and the engineering applications of the generalized half-normal model via an adaptive progressive hybrid censored mechanism

“…Moreover, it has been known to be simpler to manipulate than other priors as it adapts appropriately to the support of the parameters. The posterior distribution of α and σ can be expressed by combining the likelihood function in (6) and the joint prior distribution in (12) as ARTICLE pubs.aip.org/aip/adv…”

“…The test stops at the time of the mth failure Xm:m:n, and at this point, all the remaining items are removed, i.e., Rm = n − m − ∑ m−1 i=1 Ri. Several publications on estimating the unknown parameters for various distributions under this censoring approach have recently appeared, see, for example, that of Balakrishnan et al, 6 Basak et al, 7 Ahmed, 8 Alotaibi et al, 9 Alotaibi et al, 10,11 and Elgarhy et al 12,13 Kundu and Joarder 14 proposed a progressive type-I hybrid censoring technique that has the same schematic representation as the P-II-C scheme but terminates testing at T * = min(T, Xm:m:n), where T is a fixed duration. The primary problem in this design is that the required sample size is random and may end up being quite small.…”