Classical and Bayesian Inference of an Exponentiated Half-Logistic Distribution under Adaptive Type II Progressive Censoring

Abstract

The point and interval estimations for the unknown parameters of an exponentiated half-logistic distribution based on adaptive type II progressive censoring are obtained in this article. At the beginning, the maximum likelihood estimators are derived. Afterward, the observed and expected Fisher’s information matrix are obtained to construct the asymptotic confidence intervals. Meanwhile, the percentile bootstrap method and the bootstrap-t method are put forward for the establishment of confidence intervals. With respect to Bayesian estimation, the Lindley method is used under three different loss functions. The importance sampling method is also applied to calculate Bayesian estimates and construct corresponding highest posterior density (HPD) credible intervals. Finally, numerous simulation studies are conducted on the basis of Markov Chain Monte Carlo (MCMC) samples to contrast the performance of the estimations, and an authentic data set is analyzed for exemplifying intention.

Reliability Analysis and Its Applications for a Newly Improved Type-II Adaptive Progressive Alpha Power Exponential Censored Sample

“…Following that, the Bayes-MCMC estimates and associated 95% HPD intervals of α, µ, R(t), or h(t) are produced using the 'coda' package. In regard to two criteria, namely, prior mean and prior variance, two sets labeled Prior 1 and 2 of the hyperparameters (a 1 , a 2 , b 1 , b 2 ) are taken as (2.5, 7.5, 5, 5) and (5,15,10,10), respectively.…”

“…In light of this, Ng et al [7] presented an adaptive PT-IIC to improve statistical analysis efficiency. In this plan, the number of failures m is decided in advance, and the testing time is allowed to exceed the threshold T. Many academics have studied this strategy due to its exceptional benefits; see, for example, Panahi and Moradi [8], Kohansal and Shoaee [9], Xiong and Gui [10], and Du and Gui [11], among others.…”

Cure Model for End-Stage Chronic Kidney Disease Patients at Benjamin Mkapa Hospital, Dodoma,Tanzania

“…Therefore, this study used the exponentiated half-logistic distribution as a baseline distribution to fit cure model for end stage chronic kidney disease patients at Benjamin Mkapa Hospital. The exponentiated half-logistic distribution is commonly applied in different fields such as insurance, engineering, medicine and education [21]. This distribution is robust and suitable for modelling life time data because it is related to different distributions like exponential distribution, Pareto distribution with two parameters, uniform distribution, Weibull distribution with two parameters, logistic distribution and Gumbel distribution with two parameters [18].…”

“…For this reason, EHLD was opted as the baseline distribution for cure model. According to [21] if T is a random variable that follows a two parameter EHLD then, the cumulative distribution function 𝐹(𝑡), the probability density function 𝑓(𝑡), survival function 𝑆(𝑡) and hazard rate function ℎ(𝑡) of EHLD are given as follows:…”

Bayesian and Non-Bayesian Inference for Unit-Exponentiated Half-Logistic Distribution with Data Analysis

“…Jeon and Kang [28] used multiple Type-I hybrid censoring to look at estimators of the EHLD parameters. Adaptive progressive censoring was used by Xiong and Gui [29] to investigate the parameter estimators of the EHLD. The goal of this essay is to construct a new probability, called the unit-EHLD (UEHLD) by using transformation T = e −Y , where Y is the EHLD.…”