Maximum likelihood estimation of the generalised Gompertz distribution under progressively first-failure censored sampling

In this paper, the maximum likelihood estimators of the unknown parameters, as well as some lifetime parameters survival and hazard rate functions, of a three-parameter generalised Gompertz lifetime model based on progressively first-failure censored sampling are obtained. Approximate confidence intervals for the unknown parameters and the reliability characteristics are constructed based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators. Although the proposed estimators cannot be expressed in explicit forms, these can be easily obtained through the use of appropriate numerical techniques. Finally, a real data set has been analysed for illustrative purposes

Statistical analysis of progressively first-failure-censored data via beta-binomial removals

Progressive first-failure censoring has been widely-used in practice when the experimenter desires to remove some groups of test units before the first-failure is observed in all groups. Practically, some test groups may haphazardly quit the experiment at each progressive stage, which cannot be determined in advance. As a result, in this article, we propose a progressively first-failure censored sampling with random removals, which allows the removal of the surviving group(s) during the execution of the life test with uncertain probability, called the beta-binomial probability law. Generalized extreme value lifetime model has been widely-used to analyze a variety of extreme value data, including flood flows, wind speeds, radioactive emissions, and others. So, when the sample observations are gathered using the suggested censoring plan, the Bayes and maximum likelihood approaches are used to estimate the generalized extreme value distribution parameters. Furthermore, Bayes estimates are produced under balanced symmetric and asymmetric loss functions. A hybrid Gibbs within the Metropolis-Hastings method is suggested to gather samples from the joint posterior distribution. The highest posterior density intervals are also provided. To further understand how the suggested inferential approaches actually work in the long run, extensive Monte Carlo simulation experiments are carried out. Two applications of real-world datasets from clinical trials are examined to show the applicability and feasibility of the suggested methodology. The numerical results showed that the proposed sampling mechanism is more flexible to operate a classical (or Bayesian) inferential approach to estimate any lifetime parameter

Bayesian and Classical Inference under Type-II Censored Samples of the Extended Inverse Gompertz Distribution with Engineering Applications

In this article, we introduce a new three-parameter distribution called the extended inverse-Gompertz (EIGo) distribution. The implementation of three parameters provides a good reconstruction for some applications. The EIGo distribution can be seen as an extension of the inverted exponential, inverse Gompertz, and generalized inverted exponential distributions. Its failure rate function has an upside-down bathtub shape. Various statistical and reliability properties of the EIGo distribution are discussed. The model parameters are estimated by the maximum-likelihood and Bayesian methods under Type-II censored samples, where the parameters are explained using gamma priors. The performance of the proposed approaches is examined using simulation results. Finally, two real-life engineering data sets are analyzed to illustrate the applicability of the EIGo distribution, showing that it provides better fits than competing inverted models such as inverse-Gompertz, inverse-Weibull, inverse-gamma, generalized inverse-Weibull, exponentiated inverted-Weibull, generalized inverted half-logistic, inverted-Kumaraswamy, inverted Nadarajah–Haghighi, and alpha-power inverse-Weibull distributions

Bayesian and Non-Bayesian Estimation for Weibull Parameters Based on Generalized Type-II Progressive Hybrid Censoring Scheme

Bayesian and non-Bayesian estimators are obtained for the unknown parameters of Weibull distribution based on the generalized Type-II progressive hybrid censoring scheme and different special cases are obtained. The asymptotic variance covariance matrix and approximate confidence intervals based on the asymptotic normality of the maximum likelihood estimators are obtained. Bayes estimates and Bayes risks have been developed under a squared error loss function using informative and non-informative priors for the unknown Weibull parameters. It is observed that the estimators obtained are not available in closed forms, although they can be easily evaluated for a given sample by using suitable numerical methods. Therefore, a numerical example is considered to illustrate the proposed estimators

Bayesian Life Analysis of Generalized Chen's Population Under Progressive Censoring: Generalized Chen's Population Under Progressive Censoring

Chen's model with bathtub shape provides an appropriate conceptual for the hazard rate of various industrial products and clinical cases. This article deals with the problem of estimating the model parameters, reliability and hazard functions of a three-parameter Chen distribution based on progressively Type-II censored sample have been obtained. Based on the s-normal approximation to the asymptotic distribution of the maximum likelihood estimates and log-transformed maximum likelihood estimates, the approximate confidence intervals for the unknown parameters, and any function of them, are constructed. Using independent gamma conjugate priors, the Bayes estimators of the unknown parameters and reliability characteristics are derived under different versions of a symmetric squared error loss functions. However, the Bayes estimators are obtained in a complex form, so we have been used Metropolis-Hastings sampler procedure to carry out the Bayes estimates and also to construct the corresponding credible intervals. To assess the performance of the proposed estimators, numerical results using Monte Carlo simulation study were reported. To determine the optimum censoring scheme among different competing censoring plans, some optimality criteria have been considered. A practical example using real-life data set, representing the survival times of head and neck cancer patients, is discussed to demonstrate how the applicability of the proposed methods in real phenomenon

Statistical Analysis of Inverse Weibull Constant-Stress Partially Accelerated Life Tests with Adaptive Progressively Type I Censored Data

In life-testing investigations, accelerated life testing is crucial since it reduces both time and costs. In this study, constant-stress partially accelerated life tests using adaptive progressively Type I censored samples are taken into account. This is accomplished under the assumption that the lifespan of products under normal use conditions follows the inverse Weibull distribution. In addition to using the maximum likelihood approach, the maximum product of the spacing procedure is utilized to obtain the point and interval estimates of the model parameters as well as the acceleration factor. Employing the premise of independent gamma priors, the Bayes point estimates using the squared error loss function and the Bayes credible intervals are obtained based on both the likelihood and product of spacing functions via the Markov chain Monte Carlo technique. To assess the effectiveness of the various approaches, a simulation study is used because it is not possible to compare the findings theoretically. To demonstrate the applicability of the various approaches, two real datasets for the lifetime of micro-droplets in the ambient environment and light-emitting diode failure data are investigated. Based on the numerical results, to estimate the parameters and acceleration factor of the inverse Weibull distribution based on the suggested scheme with constant-stress partially accelerated life tests, it is recommended to utilize the Bayesian estimation approach

Analysis for Xgamma Parameters of Life under Type-II Adaptive Progressively Hybrid Censoring with Applications in Engineering and Chemistry

Censoring mechanisms are widely used in various life tests, such as medicine, engineering, biology, etc., as they save (overall) test time and cost. In this context, we consider the problem of estimating the unknown xgamma parameter and some survival characteristics, such as reliability and failure rate functions in the presence of adaptive type-II progressive hybrid censored data. For this purpose, the maximum likelihood and Bayesian inferential approaches are used. Using the observed Fisher information under s-normal approximation, different asymptotic confidence intervals for any function of the unknown parameter were constructed. Using the gamma flexible prior, Bayes estimators against the squared-error loss were developed. Two procedures of Bayesian approximations—Lindley’s approximation and Metropolis–Hastings algorithm—were used to carry out the Bayes estimates and to construct the associated credible intervals. An extensive simulation study was implemented to compare the performance of the different methods. To validate the proposed methodologies of inference—two practical studies using datasets that form engineering and chemical fields are discussed

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

A new two-parameter extended exponential lifetime distribution with an increasing failure rate called the Poisson–exponential (PE) model was explored. In the reliability experiments, an adaptive progressively Type-II hybrid censoring strategy is presented to improve the statistical analysis efficiency and reduce the entire test duration on a life-testing experiment. To benefit from this mechanism, this paper sought to infer the unknown parameters, as well as the reliability and failure rate function of the PE distribution using both the likelihood and product of spacings estimation procedures as a conventional view. For each unknown parameter, from both classical approaches, an approximate confidence interval based on Fisher’s information was also created. Additionally, in the Bayesian paradigm, the given classical approaches were extended to Bayes’ continuous theorem to develop the Bayes (or credible interval) estimates of the same unknown quantities. Employing the squared error loss, the Bayesian inference was developed based on independent gamma assumptions. Because of the complex nature of the posterior density, the Markov chain with the Monte Carlo methodology was used to obtain data from the whole conditional distributions and, therefore, evaluate the acquired Bayes point/interval estimates. Via extensive numerical comparisons, the performance of the estimates provided was evaluated with respect to various criteria. Among different competing progressive mechanisms, using four optimality criteria, the best censoring was suggested. Two real chemical engineering datasets were also analyzed to highlight the applicability of the acquired point and interval estimators in an actual practical scenario

Inferences for Nadarajah–Haghighi Parameters via Type-II Adaptive Progressive Hybrid Censoring with Applications

This study aims to investigate the estimation problems when the parent distribution of the population under consideration is the Nadarajah–Haghighi distribution in the presence of an adaptive progressive Type-II hybrid censoring scheme. Two approaches are considered in this regard, namely, the maximum likelihood and Bayesian estimation methods. From the classical point of view, the maximum likelihood estimates of the unknown parameters, reliability, and hazard rate functions are obtained as well as the associated approximate confidence intervals. On the other hand, the Bayes estimates are obtained based on symmetric and asymmetric loss functions. The Bayes point estimates and the highest posterior density Bayes credible intervals are computed using the Monte Carlo Markov Chain technique. A comprehensive simulation study is implemented by proposing different scenarios for sample sizes and progressive censoring schemes. Moreover, two applications are considered by analyzing two real data sets. The outcomes of the numerical investigations show that the Bayes estimates using the general entropy loss function are preferred over the other methods

Computational Analysis for Fréchet Parameters of Life from Generalized Type-II Progressive Hybrid Censored Data with Applications in Physics and Engineering

Generalized progressive hybrid censored procedures are created to reduce test time and expenses. This paper investigates the issue of estimating the model parameters, reliability, and hazard rate functions of the Fréchet (Fr) distribution under generalized Type-II progressive hybrid censoring by making use of the Bayesian estimation and maximum likelihood methods. The appropriate estimated confidence intervals of unknown quantities are likewise built using the frequentist estimators’ normal approximations. The Bayesian estimators are created using independent gamma conjugate priors under the symmetrical squared-error loss. The Bayesian estimators and the associated greatest posterior density intervals cannot be computed analytically since the joint likelihood function is obtained in complex form, but they may be assessed using Monte Carlo Markov chain (MCMC) techniques. Via extensive Monte Carlo simulations, the actual behavior of the proposed estimation methodologies is evaluated. Four optimality criteria are used to choose the best censoring scheme out of all the options. To demonstrate how the suggested approaches may be utilized in real scenarios, two real applications reflecting the thirty successive values of precipitation in Minneapolis–Saint Paul for the month of March as well as the number of vehicle fatalities for thirty-nine counties in South Carolina during 2012 are examined