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Modeling the failure times of processors and memories in computers is crucial for ensuring the reliability and robustness of data science workflows. By understanding the failure characteristics of the hardware components, data scientists can develop strategies to mitigate the impact of failures on their computations, and design systems that are more fault-tolerant and resilient. In particular, failure time modeling allows data scientists to predict the likelihood and frequency of hardware failures, which can help inform decisions about system design and resource allocation. In this paper, we aimed to model the failure times of processors and memories of computers; this was performed by formulating a new type of bivariate model using the copula function. The modified extended exponential distribution is the suggested lifetime of the experimental units. It was shown that the new bivariate model has many important properties, which are presented in this work. The inferential statistics for the distribution parameters were obtained under the assumption of a Type-II censored sampling scheme. Therefore, point and interval estimation were observed using the maximum likelihood and the Bayesian estimation methods. Additionally, bootstrap confidence intervals were calculated. Numerical analysis via the Markov Chain Monte Carlo method was performed. Finally, a real data example of processors and memories failure time was examined and the efficiency of the new bivariate distribution of fitting the data sample was observed by comparing it with other bivariate models. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate the unknown parameters of weighted exponential distribution based on the competing risks model under progressively Type-II censoring. It is supposed that the latent causes of failures have weighted exponential distributions with different parameters. The maximum likelihood estimations of four unknown parameters are derived and the uniqueness and existence of them are theoretically proved. Moreover, approximate intervals are proposed and constructed with the delta method and Fisher information matrix. Bootstrap methods are also applied to calculate the confidence intervals. Furthermore, Bayes estimates and the corresponding credible intervals under three various loss functions are computed by using the Monte Carlo Markov Chain method. A simulation study is conducted to assess the statistical performance of all the estimators. Ultimately, real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. [ABSTRACT FROM AUTHOR]

Here in this paper, we consider the progressive Type-II censoring Gompertz data under competing risks model with binomial removals. The maximum likelihood estimators of the model parameters involved are obtained by applying numerical methods and the asymptotic variance-covariance matrix of the estimates is also derived. Bayesian estimates based on importance sampling procedure are developed under squared error, LINEX and general entropy loss functions. The confidence intervals using the asymptotic normality and Bayesian approaches are also developed. Finally, a Monte Carlo simulation is conducted to evaluate the performance of the so proposed estimators under all these different estimation methods. [ABSTRACT FROM AUTHOR]

In this paper, classical and Bayesian estimation for the parameters and the reliability function for the generalized logarithmic transformation exponential (GLTE) distribution has been proposed when the life-times are progressively censored. The maximum likelihood estimator of unknown parameters and their corresponding reliability function are obtained under the classical setup. The Bayes estimators are obtained for symmetric (squared error) and asymmetric (LINEX and general entropy) loss functions. This was achieved by considering discrete prior for the scale parameter and conditional gamma prior for the shape parameter. Interval estimation of the unknown parameters and reliability function for classical and Bayesian schemes is also considered. The performances of various derived estimators are recorded using simulation study for different sample sizes and progressive censoring schemes. Finally, the COVID-19 mortality data sets are provided to illustrate the computation of various estimators. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the exponentiated generalized alpha power family of distributions to extend several other distributions. We use the new family and develop a new distribution, called the exponentiated generalized alpha power exponential (EGAPEx) distribution. The proposed EGAPEx distribution provides greater flexibility in modeling data from a practical point of view. The new model includes the exponential; alpha power exponential; alpha power generalized exponential, generalized exponential, standardized generalized exponential and exponentiated generalized exponential distributions as a special cases. This distribution exhibits four hazard rate shapes such as L shaped, increasing, decreasing, and upside-down bathtub. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by maximum likelihood, maximum product spacing, and Bayesian estimation methods. In addition, we have obtained approximate confidence intervals, two bootstrap confidence intervals, and Bayes credible intervals. A Monte Carlo Simulation is performed to compare the different methods of estimation. We illustrate the performance of the proposed distribution through two real data sets; one is related to economic data and another is failure time data and the data sets show the proposed distribution is superior in its ability to model the data sets as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions. [ABSTRACT FROM AUTHOR]

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In this paper, based on an adaptive Type-II progressively censored sample from the generalized exponential distribution, the maximum likelihood and Bayesian estimators are derived for the unknown parameters as well as the reliability and hazard functions. Also, the approximate confidence intervals of the unknown parameters, and the reliability and hazard functions are calculated. Markov chain Monte Carlo method is applied to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Moreover, results from simulation studies assessing the performance of our proposed method are included. Finally, an illustrative example using real data set is presented for illustrating all the inferential procedures developed here. [ABSTRACT FROM AUTHOR]

In life testing and reliability studies, most researchers have used the maximum likelihood estimation method to estimate unknown parameters, even though it has been proven that the maximum product of spacing method has properties as good as the maximum likelihood estimation method and sometimes even better. In this study, we aim to estimate the unknown parameters of the modified Kies exponential distribution along with the reliability and hazard rate functions under progressive type-II censoring scheme. The maximum likelihood and maximum product of spacing methods are considered in order to find the point estimates and approximate confidence intervals of the various parameters. Moreover, Bayesian estimations based on the likelihood function and the product of the spacing function of the unknown parameters are obtained using the squared error loss function with independent gamma priors. It is observed that the joint posterior distributions have complicated forms. Because of this, Lindley's approximation and the Markov chain Monte Carlo technique are used to obtain the Bayesian estimates and highest posterior credible intervals. Monte Carlo simulations are performed in order to evaluate the performance of the proposed estimation methods. Two real datasets are studied to demonstrate the efficacy of the offered methodologies and highlight how simple and applicable it might be to apply them in practical fields. [ABSTRACT FROM AUTHOR]

In this research, random censoring is employed as a methodology for parameter estimation within the context of an exponential distribution. These parameter estimations are conducted using both the Bayesian and maximum likelihood approaches. In the Bayesian framework, Lindley's approximation method is applied to derive estimates, which are subsequently assessed under three distinct balanced loss functions. To gauge the efficacy of different estimation techniques, simulation-based investigations are conducted. Additionally, a real-world data analysis is executed to illustrate the practical applicability of these methodologies. The findings consistently underscore the superiority of Bayesian parameter estimates in comparison with their maximum likelihood counterparts across all analyzed methodologies. [ABSTRACT FROM AUTHOR]

In this paper inverted Kumaraswamy distribution is introduced. Some of its properties are presented through, some models of stress strength, measures of central tendency and dispersion and order statistics. Some sub-models, limiting distributions and the relation between inverted Kumaraswamy and other distributions are derived. The maximum likelihood and Bayes estimators, confidence intervals for the parameters, the reliability and the hazard rate functions of the inverted Kumaraswamy distribution based on Type II censored samples are obtained. A numerical study is carried out to illustrate the theoretical results for both approaches, the maximum likelihood and the Bayesian estimation. Moreover, the results are applied on real data. [ABSTRACT FROM AUTHOR]

In this article, the problems of point and interval estimation for the associated parameters, along with reliability function (r(x)) and the hazard rate function (h(x)) of the inverse Gompertz distribution, are considered using a unified hybrid censoring scheme. In the case of point estimation, some classical estimators, such as the maximum likelihood estimator (MLE) and the maximum product spacing estimator (MPSE), are derived. Further, Bayes estimators are considered with respect to a suitable prior for the associated parameters under the balanced loss functions( balanced Linex loss function and balanced general entropy loss function). The asymptotic confidence intervals using the MLEs and MPSEs of the parameters are derived. Furthermore, the equal-tailed and the highest posterior density credible intervals are derived using the posterior samples. The mean squared errors are used to compare the point estimators, whereas the interval estimators are compared through their coverage probability and average lengths. Finally, a real data set is taken for application purposes. [ABSTRACT FROM AUTHOR]

We are mainly interested in estimating the stress–strength parameter, say R , when the parent distribution follows the well-known Marshall–Olkin model and the accessible data has the form of the progressively Type-II censored samples. In this case, the stress–strength parameter is free of the base distribution employed in the Marshall–Olkin model. Thus, we use the exponential distribution for simplicity. The maximum likelihood methods as well as some Bayesian approaches are used for the estimation purpose. The corresponding estimators of the latter approach are obtained by using Lindley's approximation and Gibbs sampling methods since the Bayesian estimator of R cannot be obtained as an explicit form. Moreover, some confidence intervals of various types are derived for R and then compared via a Monte Carlo simulation. Finally, the survival times of head and neck cancer patients are analyzed by two therapies for illustrating purposes. [ABSTRACT FROM AUTHOR]

The statistical inference of the reliability and parameters of the stress–strength model has received great attention in the field of reliability analysis. When following the generalized progressive hybrid censoring (GPHC) scheme, it is important to discuss the point estimate and interval estimate of the reliability of the multicomponent stress–strength (MSS) model, in which the stress and the strength variables are derived from different distributions by assuming that stress follows the Chen distribution and that strength follows the Gompertz distribution. In the present study, the Newton–Raphson method was adopted to derive the maximum likelihood estimation (MLE) of the model parameters, and the corresponding asymptotic distribution was adopted to construct the asymptotic confidence interval (ACI). Subsequently, the exact confidence interval (ECI) of the parameters was calculated. A hybrid Markov chain Monte Carlo (MCMC) method was adopted to determine the approximate Bayesian estimation (BE) of the unknown parameters and the high posterior density credible interval (HPDCI). A simulation study with the actual dataset was conducted for the BEs with squared error loss function (SELF) and the MLEs of the model parameters and reliability, comparing the bias and mean squares errors (MSE). In addition, the three interval estimates were compared in terms of the average interval length (AIL) and coverage probability (CP). [ABSTRACT FROM AUTHOR]

Bayesian estimation of the parameters in beta mixture models (BMM) is analytically intractable. The numerical solutions to simulate the posterior distribution are available, but incur high computational cost. In this paper, we introduce an approximation to the prior/posterior distribution of the parameters in the beta distribution and propose an analytically tractable (closed form) Bayesian approach to the parameter estimation. The approach is based on the variational inference (VI) framework. Following the principles of the VI framework and utilizing the relative convexity bound, the extended factorized approximation method is applied to approximate the distribution of the parameters in BMM. In a fully Bayesian model where all of the parameters of the BMM are considered as variables and assigned proper distributions, our approach can asymptotically find the optimal estimate of the parameters posterior distribution. Also, the model complexity can be determined based on the data. The closed-form solution is proposed so that no iterative numerical calculation is required. Meanwhile, our approach avoids the drawback of overfitting in the conventional expectation maximization algorithm. The good performance of this approach is verified by experiments with both synthetic and real data. [ABSTRACT FROM AUTHOR]