This study focuses on estimating the reliability of a multicomponent stress-strength model using two Bayesian approaches‎: ‎E-Bayesian and hierarchical Bayesian‎. ‎This model follows Inverse Rayleigh distributions with distinct parameters‎. ‎Additionally‎, ‎the efficiency of the proposed methods is compared by employing Monte Carlo simulation and analyzing a data set.

‎The recent advancements in technology have faced an increase in the growth rate of data‎.‎According to the amount of data generated‎, ‎ensuring effective analysis using traditional approaches becomes very complicated‎.‎One of the methods of managing and analyzing big data is classification‎.‎%One of the data mining methods used commonly and effectively to classify big data is the MapReduce‎‎In this paper‎, ‎the feature weighting technique to improve Bayesian classification algorithms for big data is developed based on Correlative Naive Bayes classifier and MapReduce Model‎.‎%Classification models include Naive Bayes classifier‎, ‎correlated Naive Bayes and correlated Naive Bayes with feature weighting‎.‎Correlated Naive Bayes classification is a generalization of the Naive Bayes classification model by considering the dependence between features‎.‎%This paper uses the feature weighting technique and Laplace calibration to improve the correlated Naive Bayes classification‎.‎The performance of all described methods are evaluated by considering accuracy‎, ‎sensitivity and specificity‎, ‎accuracy‎, ‎sensitivity and specificity metrics.

This article examines statistical inference for R= P(Y<X) where X and Y are independent but not identically distributed Pareto of the first kind (Pareto (I)) random variables with same scale parameter but different shape parameters. The Maximum likelihood, uniformly minimum variance unbiased and Bayes estimators with Gamma prior are used for this purpose. Simulation studies which compare the estimators are presented. Moreover, sensitivity of Bayes estimator to the prior parameters is considered.

In the estimation of a probability density function (PDF) by kernel method, two inherent problems are the choice of sampling methods and the selection of a bandwidth. In this article, we use the balanced and unbalanced ranked set sampling (RSS) methods and Bayesian bandwidth to estimate a PDF by kernel method. To compare our method with existing methods, we use an extensive simulation study to compare the RSS with simple random sampling (SRS) PDF estimator and also Bayesian bandwidth with other existing bandwidths. As an application, we use the household expenses and income data of the Statistical Center of Iran in 2021 to estimate the PDF of the total expenses of the households in Tehran province.

To study the heterogeneous nature of lifetimes of certain mechanical or engineering processes, a mixture model of some suitable lifetime distributions may be more appropriate and appealing as com-pared to simple models. This paper considers mixture of Topp-Leone distributions under classical and Bayesian perspective based on com-plete sample. The new distribution which exhibits decreasing and up-side down bathtub shaped density while the distribution has the ability to model lifetime data with decreasing, increasing and upside down bathtub shaped failure rates. We derive several properties of the new distribution such as moments, moment generating function, conditional moment, mean deviation, Bonferroni and Lorenz curves and the order statistics of the proposed distribution. Moreover, we estimate the pa-rameters of the model by using frequentist and Bayesian approaches. For Bayesian analysis, , ve loss functions, namely the squared error loss function (SELF), weighted squared error loss function (WSELF), mod-i, ed squared error loss function (MSELF), precautionary loss function (PLF), and K-loss function (KLF) and uniform as well as gamma pri-ors are considered to obtain the Bayes estimators and posterior risk of the unknown parameters of the model. Furthermore, credible intervals (CIs) and highest posterior density (HPD) intervals are also obtained. Monte Carlo simulation study is done to access the behavior of these estimators. For the illustrative purposes, a real-life application of the proposed distribution to a tensile strength data set is provided.