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

Stress-strength reliability estimation for the inverted exponentiated Rayleigh distribution under unified progressive hybrid censoring with application

In this paper, we studied the estimation of a stress-strength reliability model (R = P(X>Y)) based on inverted exponentiated Rayleigh distribution under the unified progressive hybrid censoring scheme (unified PHCS). The maximum likelihood estimates of the unknown parameters were obtained using the stochastic expectation-maximization algorithm (stochastic EMA). The asymptotic confidence intervals were also created. Under squared error and Linex and generalized entropy loss functions, the Gibbs sampler together with Metropolis-Hastings algorithm was provided to compute the Bayes estimates and the credible intervals. Extensive simulations were performed to see the effectiveness of the proposed estimation methods. Also, parallel to the development of reliability studies, it is necessary to study its application in different sciences such as engineering. Therefore, droplet splashing data under two nozzle pressures were proposed to exemplify the theoretical outcomes

Estimation and Prediction for Type-II Hybrid Censored Data Follow Flexible Weibull Distribution

In this paper, we proposed Bayes estimators for estimating the parameters, reliability, hazard rate, mean time to failure from flexible Weibull distribution using Type-II hybrid censored sample. Bayes estimators have been obtained under squared error loss function assuming independent gamma prior distributions for the parameters. The maximum likelihood estimators along with asymptotic distributions have also been discussed. The performances of the estimators have been compared with respect to the various Type-II hybrid censoring schemes. For approximating the posteriors, we proposed the use of Markov chain Monte Carlo techniques such as Gibbs sampler and Metropolis-Hastings algorithm. Further, Bayesian One- andTwo-sample prediction problems have also been considered. A real data set has been analysed for illustration purposes

Parameter Estimation and Prediction of Future Failures in the Log-Logistic Distributions Based on Hybrid-Censored Data

The main purpose of this thesis is to study the prediction of future observations of a Log-Logistic distribution from Hybrid Censored Samples. We will study parameter point estimation, interval estimation, different point predictors will be formed such as Maximum Likelihood Predictor (MLP), Best Unbiased Predictor (BUP), and Conditional Median Predictor (CMP). Different Prediction intervals will be constructed such as Intervals based on Pivotal quantities, and High-Density Intervals (HDI). A simulation study will be run using the R software to investigate and compare the performance of all point predictors and prediction intervals. It is observed that the (BUP) is the best point predictor and the (HDI) is the best prediction interval

Inference About The Generalized Exponential Quantiles Based On Progressively Type-Ii Censored Data

In this study, we are interested in investigating the performance of likelihood inference procedures for the ℎ quantile of the Generalized Exponential distribution based on progressively censored data. The maximum likelihood estimator and three types of classical confidence intervals have been considered, namely asymptotic, percentile, and bootstrap-t confidence intervals. We considered Bayesian inference too. The Bayes estimator based on the squared error loss function and two types of Bayesian intervals were considered, namely the equal tailed interval and the highest posterior density interval. We conducted simulation studies to investigate and compare the point estimators in terms of their biases and mean squared errors. We compared the various types of intervals using their coverage probability and expected lengths. The simulations and comparisons were made under various types of censoring schemes and sample sizes. We presented two examples for data analysis, one of them is based on simulated data set and the other one based on a real lifetime data. Finally, we compared the classical inference and the Bayesian inference procedures. We concluded that Bias and MSE for classical statistics estimators show bitter results than the Bayesian estimators. Also, Bayesian intervals which attain the nominal error rate have the best average widths. We presented our conclusions and discussed ideas for possible future research

Estimation of the Parameters of the Generalized Inverted Exponential Distribution with Progressive type I Interval Censored Data

In this article, we study estimation methodologies for parameters of a generalized inverted exponentialdistribution based on different estimation methods using progressively type I interval censored data. Inthis approach, besides conventional maximum likelihood estimation, mid-point method, probability plotmethod and method of moments are proposed for parameter estimation. To obtain maximum likelihood esti-mates, we use Newton-Raphson, expectation-maximization and stochastic expectation-maximization meth-ods. Moreover, the approximate confidence intervals of the parameters are obtained via the inverse of theobserved information matrix. In addition, percentile bootstrap technique is utilized to compute confidenceintervals. Numerical comparisons are presented of the proposed estimators using Monte Carlo simulation-s. To demonstrate the proposed methodology in a real-life scenario, survival times of guinea pigs injectedwith different doses of tubercle bacilli data is considered to show the applicability of the proposed methods.Finally, different methods for determining the inspection times and optimal censoring planes are studied.Estimation of the Parameters of the Generalized Inverted ExponentialDistribution with Progressive type I Interval Censored Dat