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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 ranked set sampling (RSS) is an efficient and flexible sampling method. Based on a modified RSS named minimum ranked set sampling samples (MinRSSU), inference of a dependent competing risks model is proposed in this paper. Then, Marshall–Olkin bivariate distribution model is used to describe the dependence of competing risks. When the competing risks data follow the proportional hazard rate distribution, a dependent competing risks model based on MinRSSU sampling is constructed. In addition, the model parameters and reliability indices were estimated by the classical and Bayesian method. Maximum likelihood estimators and corresponding asymptotic confidence intervals are constructed by using asymptotic theory. In addition, the Bayesian estimator and highest posterior density credible intervals are established under the general prior. Furthermore, according to E-Bayesian theory, the point and interval estimators of model parameters and reliability indices are obtained by a sampling algorithm. Finally, extensive simulation studies and a real-life example are presented for illustrations. [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]

Copula models are increasingly recognized for their ability to capture complex dependencies among random variables. In this study, we introduce three innovative bivariate models utilizing copula functions: the XLindley (XL) distribution with Frank, Gumbel, and Clayton copulas. The results highlight the fundamental characteristics and effectiveness of these newly introduced bivariate models. Statistical inference for the distribution parameters is conducted using a Type II censored sampling design. This employs maximum likelihood and Bayesian estimation techniques. Asymptotic and credible confidence intervals are calculated, and numerical analysis is performed using the Markov Chain Monte Carlo method. The proposed methodology's applicability is illustrated by analyzing several real-world datasets. The initial dataset examines burr formation occurrences and consists of two observation sets. Additionally, the second and third datasets contain medical information. The second dataset focuses on diabetic nephropathy, while the third dataset explores infection and recurrence time among kidney patients. [ABSTRACT FROM AUTHOR]

In survival analyses, infections at the catheter insertion site among kidney patients using portable dialysis machines pose a significant concern. Understanding the bivariate infection recurrence process is crucial for healthcare professionals to make informed decisions regarding infection management protocols. This knowledge enables the optimization of treatment strategies, reduction in complications associated with infection recurrence and improvement of patient outcomes. By analyzing the bivariate infection recurrence process in kidney patients undergoing portable dialysis, it becomes possible to predict the probability, timing, risk factors and treatment outcomes of infection recurrences. This information aids in identifying the likelihood of future infections, recognizing high-risk patients in need of close monitoring, and guiding the selection of appropriate treatment approaches. Limited bivariate distribution functions pose challenges in jointly modeling inter-correlated time between recurrences with different univariate marginal distributions. To address this, a Copula-based methodology is presented in this study. The methodology introduces the Kavya–Manoharan transformation family as the lifetime model for experimental units. The new bivariate models accurately measure dependence, demonstrate significant properties, and include special sub-models that leverage exponential, Weibull, and Pareto distributions as baseline distributions. Point and interval estimation techniques, such as maximum likelihood and Bayesian methods, where Bayesian estimation outperforms maximum likelihood estimation, are employed, and bootstrap confidence intervals are calculated. Numerical analysis is performed using the Markov chain Monte Carlo method. The proposed methodology's applicability is demonstrated through the analysis of two real-world data-sets. The first data-set, focusing on infection and recurrence time in kidney patients, indicates that the Farlie–Gumbel–Morgenstern bivariate Kavya–Manoharan–Weibull (FGMBKM-W) distribution is the best bivariate model to fit the kidney infection data-set. The second data-set, specifically that related to UEFA Champions League Scores, reveals that the Clayton Kavya–Manoharan–Weibull (CBKM-W) distribution is the most suitable bivariate model for fitting the UEFA Champions League Scores. This analysis involves examining the time elapsed since the first goal kicks and the home team's initial goal. [ABSTRACT FROM AUTHOR]

This paper attempts to estimate the parameters for the two-parameter Rayleigh distribution based on adaptive Type II progressive hybrid censored data with competing risks. Firstly, the maximum likelihood function and the maximum likelihood estimators are derived before the existence and uniqueness of the latter are proven. Further, Bayesian estimators are considered under symmetric and asymmetric loss functions, that is the squared error loss function, the LINEXloss function, and the general entropy loss function. As the Bayesian estimators cannot be obtained explicitly, the Lindley method is applied to compute the approximate Bayesian estimates. Finally, a simulation study is conducted, and a real dataset is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

A new life performance index is proposed for evaluating the quality of lifetime products. The maximum likelihood estimation method and the Bayesian approaches using informative and non-informative prior distributions are utilized to infer the parameters of the Weibull distribution and the proposed new life performance index under a Type-I hybrid censoring scheme. Monte Carlo simulation results show that two Bayesian approaches outperform the maximum likelihood estimation method in terms of the measures of relative bias, relative mean square error, and coverage probability for the point and confidence interval estimators, respectively. The Bayesian approach using a non-informative prior distribution is recommended if the knowledge of setting up the hyper-parameters in the informative prior distribution is not available. Two real data sets are provided for illustration. [ABSTRACT FROM AUTHOR]

Left-truncated and right-censored data are widely used in lifetime experiments, biomedicine, labor economics, and actuarial science. This article discusses how to resolve the problems of statistical inferences on the unknown parameters of the exponentiated half-logistic distribution based on left-truncated and right-censored data. In the beginning, maximum likelihood estimations are calculated. Then, asymptotic confidence intervals are constructed by using the observed Fisher information matrix. To cope with the small sample size scenario, we employ the percentile bootstrap method and the bootstrap-t method for the establishment of confidence intervals. In addition, Bayesian estimations under both symmetric and asymmetric loss functions are addressed. Point estimates are computed by Tierney–Kadane's approximation and importance sampling procedure, which is also applied to establishing corresponding highest posterior density credible intervals. Lastly, simulated and real data sets are presented and analyzed to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primarily for use with biological data. The hazard rate function, quantile function, and several other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has increasing, decreasing, bathtub, and upside-down bathtub shapes. The maximum likelihood and Bayesian techniques are both used to estimate unknown parameters. Based on the proposed distribution, we also present a parametric regression model and a Bayesian regression approach. As an assessment of the longstanding performance, simulation studies based on maximum likelihood and Bayesian techniques of estimation procedures are also conducted. Two real datasets are used to demonstrate the applicability of the new distribution. The efficiency of the third parameter in the new model is tested by utilizing the likelihood ratio test. Furthermore, the parametric bootstrap approach is used to determine the effectiveness of the suggested model for the datasets. [ABSTRACT FROM AUTHOR]

In this study, a new three-statement randomized response estimation method is proposed to improve the drawback that the maximum likelihood estimation method could generate a negative value to estimate the sensitive-nature proportion (SNP) when its true value is small. The Bayes estimator of the SNP is obtained via using a hierarchical Bayesian modeling procedure. Moreover, a hybrid algorithm using Gibbs sampling in Metropolis–Hastings algorithms is used to obtain the Bayes estimator of the SNP. The highest posterior density interval of the SNP is obtained based on the empirical distribution of Markov chains. We use the term 3RR-HB to denote the proposed method here. Monte Carlo simulations show that the quality of 3RR-HB procedure is good and that it can improve the drawback of the maximum likelihood estimation method. The proposed 3RR-HB procedure is simple for use. An example regarding the homosexual proportion of college freshmen is used for illustration. [ABSTRACT FROM AUTHOR]

Using progressive first-failure censored samples, we mainly study the inferences of the unknown parameters and the reliability and failure functions of the Inverted Exponentiated Half-Logistic distribution. The progressive first-failure censoring is an extension and improvement of progressive censoring, which is of great significance in the field of lifetime research. Besides maximum likelihood estimation, we use Bayesian estimation under unbalanced and balanced losses: General Entropy loss function, Squared Error loss function and Linex loss function. Approximate explicit expression of Bayesian estimation is given using Lindley approximation method for point estimation and Metropolis-Hastings method for point and interval estimation. Bayesian credible intervals and asymptotic confidence intervals are derived in the form of average length and coverage probability. To show the research effects, a simulation study and practical data analysis are carried out. Finally, we discuss the optimal censoring mode under four different criteria. [ABSTRACT FROM AUTHOR]