Data analysis with applications in physics and engineering using XLindley model with improved adaptive Type-II progressively censored samples.

Recently, a novel improved adaptive Type-II progressive censoring strategy has been suggested in order to obtain adequate data from trials that require a lengthy amount of time. Considering this scheme, this paper focuses on various classical and Bayesian estimation challenges for parameter and some reliability metrics for the XLindley distribution. Two classical estimation methods are considered from the classical perspective to get the point and interval estimations of the model parameter as well as reliability and hazard rate functions. In addition to the usual approaches, the Bayesian methodology is looked at by leveraging the squared error loss function and the Markov chain Monte Carlo technique. The Bayes point and credible intervals are obtained based on two forms of the posterior distribution. A simulation examination is implemented adopting multiple circumstances to distinguish between the conventional and Bayesian estimations. The simulation results demonstrate that the Bayesian approach using the likelihood function is superior for estimating the model parameter when compared with the other methods. In contrast, when estimating reliability metrics, it is advisable to utilize the Bayesian method with the spacings function. Two real-world data sets are analyzed to integrate the proposed approaches into practice, and the ideal progressive censoring strategy is chosen using some optimality criteria.

Estimation procedures and optimal censoring schemes for an improved adaptive progressively type-II censored Weibull distribution.

This paper presents an effort to investigate the estimations of the Weibull distribution using an improved adaptive Type-II progressive censoring scheme. This scheme effectively guarantees that the experimental time will not exceed a pre-fixed time. The point and interval estimations using two classical estimation methods, namely maximum likelihood and maximum product of spacing, are considered to estimate the unknown parameters as well as the reliability and hazard rate functions. The approximate confidence intervals of these quantities are obtained based on the asymptotic normality of the maximum likelihood and maximum product of spacing methods. The Bayesian estimations are also considered using MCMC techniques based on the two classical approaches. An extensive simulation study is implemented to compare the performance of the different methods. Further, we propose the use of various optimality criteria to find the optimal sampling scheme. Finally, one real data set is applied to show how the proposed estimators and the optimality criteria work in real-life scenarios. The numerical outcomes demonstrated that the Bayesian estimates using the likelihood and product of spacing functions performed better than the classical estimates.

E-Bayesian Estimation Using Spacing Function for Inverse Lindley Adaptive Type-I Progressively Censored Samples: Comparative Study with Applications.

For the first time, this paper offers the Bayesian and E-Bayesian estimation methods using the spacing function (SF) instead of the classical likelihood function. The inverse Lindley distribution, including its parameter and reliability measures, is discussed in this study through the mentioned methods, along with some other classical approaches. Six-point and six-interval estimations based on an adaptive Type-I progressively censored sample are considered. The likelihood and product of spacing methods are used in classical inferential setups. The approximate confidence intervals are discussed using both classical approaches. For various parameters, the Bayesian methodology is studied by taking both likelihood and SFs as observed data sources to derive the posterior distributions. Moreover, the E-Bayesian estimation method is considered by using the same data sources in the usual Bayesian approach. The Bayes and E-Bayes credible intervals using both likelihood and SFs are also taken into consideration. Several Monte Carlo experiments are carried out to assess the performance of the acquired estimators, depending on different accuracy criteria and experimental scenarios. Finally, two data sets from the engineering and physics sectors are analyzed to demonstrate the superiority and practicality of the suggested approaches.

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.