On the Type-I Half-logistic Distribution and Related Contributions: A Review

The half-logistic (HL) distribution is a widely considered statistical model for studying lifetime phenomena arising in science, engineering, finance, and biomedical sciences. One of its weaknesses is that it has a decreasing probability density function and an increasing hazard rate function only. Due to that, researchers have been modifying the HL distribution to have more functional ability. This article provides an extensive overview of the HL distribution and its generalization (or extensions). The recent advancements regarding the HL distribution have led to numerous results in modern theory and statistical computing techniques across science and engineering. This work extended the body of literature in a summarized way to clarify some of the states of knowledge, potentials, and important roles played by the HL distribution and related models in probability theory and statistical studies in various areas and applications. In particular, at least sixty-seven flexible extensions of the HL distribution have been proposed in the past few years. We give a brief introduction to these distributions, emphasizing model parameters, properties derived, and the estimation method. Conclusively, there is no doubt that this summary could create a consensus between various related results in both theory and applications of the HL-related models to develop an interest in future studies

Some advances in life testing and reliability

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On estimating the reliability in a multicomponent system based on progressively-censored data from Chen distribution

This research deals with classical, Bayesian, and generalized estimation of stress-strength reliability parameter, Rs;k = Pr(at least s of (X1;X2; :::;Xk) exceed Y) = Pr(Xks+1:k \u3eY) of an s-out-of-k : G multicomponent system, based on progressively type-II right-censored samples with random removals when stress and strength are two independent Chen random variables. Under squared-error and LINEX loss functions, Bayes estimates are developed by using Lindley’s approximation and Markov Chain Monte Carlo method. Generalized estimates are developed using generalized variable method while classical estimates - the maximum likelihood estimators, their asymptotic distributions, asymptotic confidence intervals, bootstrap-based confidence intervals - are also developed. A simulation study and a real-world data analysis are provided to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected lengths of the confidence intervals, and biases of the estimators are also computed, compared and contrasted

Point and interval estimation for the logistic distribution based on record data

In this paper, based on record data from the two-parameter logistic distribution, the maximum likelihood and Bayes estimators for the two unknown parameters are derived. The maximum likelihood estimators and Bayes estimators can not be obtained in explicit forms. We present a simplemethod of deriving explicit maximum likelihood estimators by approximating the likelihood function. Also, an approximation based on the Gibbs sampling procedure is used to obtain the Bayes estimators. Asymptotic confidence intervals, bootstrap confidence intervals and credible intervals are also proposed. Monte Carlo simulations are performed to compare the performances of the different proposed methods. Finally, one real data set has been analysed for illustrative purposes

Statistical inferences of Rs;k = Pr(Xk-s+1:k \u3e Y ) for general class of exponentiated inverted exponential distribution with progressively type-II censored samples with uniformly distributed random removal

The problem of statistical inference of the reliability parameter Pr(Xk-s+1:k \u3e Y ) of an s-out-of-k : G system with strength components X1,X2,…,Xk subjected to a common stress Y when X and Y are independent two-parameter general class of exponentiated inverted exponential (GCEIE) progressively type-II right censored data with uniformly random removal random variables, are discussed. We use p-value as a basis for hypothesis testing. There are no exact or approximate inferential procedures for reliability of a multicomponent stress-strength model from the GCEIE based on the progressively type-II right censored data with random or fixed removals available in the literature. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed

Shrinkage Estimation and Prediction for Joint Type-II Censored Data from Two Burr-XII Populations

The main objective of this paper is to apply linear and pretest shrinkage estimation techniques to estimating the parameters of two 2-parameter Burr-XII distributions. Further more, predictions for future observations are made using both classical and Bayesian methods within a joint type-II censoring scheme. The efficiency of shrinkage estimates is compared to maximum likelihood and Bayesian estimates obtained through the expectation-maximization algorithm and importance sampling method, as developed by Akbari Bargoshadi et al. (2023) in "Statistical inference under joint type-II censoring data from two Burr-XII populations" published in Communications in Statistics-Simulation and Computation". For Bayesian estimations, both informative and non-informative prior distributions are considered. Additionally, various loss functions including squared error, linear-exponential, and generalized entropy are taken into account. Approximate confidence, credible, and highest probability density intervals are calculated. To evaluate the performance of the estimation methods, a Monte Carlo simulation study is conducted. Additionally, two real datasets are utilized to illustrate the proposed methods.Comment: 33 pages and 33 table