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In this present work, we propose the expected Bayesian and hierarchical Bayesian approaches to estimate the shape parameter and hazard rate under a generalized progressive hybrid censoring scheme for the Kumaraswamy distribution. These estimates have been obtained using gamma priors based on various loss functions such as squared error, entropy, weighted balance, and minimum expected loss functions. An investigation is carried out using Monte Carlo simulation to evaluate the effectiveness of the suggested estimators. The simulation provides a quantitative assessment of the estimates accuracy and efficiency under various conditions by comparing them in terms of mean squared error. Additionally, the monthly water capacity of the Shasta reservoir is examined to offer real-world examples of how the suggested estimations may be used and performed.

In this paper, Expected Bayesian and Hierarchical Bayesian techniques have been discussed to estimate the shape parameter of the inverse power Lomax distribution. The proposed estimates for the shape parameter are obtained by using an informative gamma prior based on squared error, entropy and weighted balance loss functions. The definitions of the proposed estimators as well as their characteristics are provided. A Monte Carlo simulation is executed to compare the performance of the proposed estimators in terms of mean squared error. Finally a real life data set has been analyzed for further illustrations. En este artículo, se analizan las técnicas bayesiana esperada y bayesiana jerárquica para estimar el parámetro de forma de la distribución Lomax de potencia inversa. Las estimaciones propuestas para el parámetro de forma se obtienen utilizando una distribución gamma previa informativa basada en el error cuadrático, la entropía y las funciones de pérdida de balance ponderadas. Se proporcionan las definiciones de los estimadores propuestos, así como sus características. Se ejecuta una simulación de Monte Carlo para comparar el rendimiento de los estimadores propuestos en términos de error cuadrático medio. Finalmente, se analiza un conjunto de datos reales para obtener más ejemplos.

PurposeImatinib is indicated for treatment of CML, GIST, etc. The population pharmacokinetics (popPK) of imatinib in patients under long-term treatment are reported in literature. Data obtained from bioequivalence trials for healthy subjects were used to evaluate the influence of demographic and pharmacogenetic factors on imatinib pharmacokinetics (PK) in a collective without concurrent drugs, organ dysfunction, inflammation etc. In addition, the differences in PK between the healthy subjects and a patient cohort was examined to identify possible disease effects.Methods26 volunteers were administered orally with single dose of 400 mg imatinib. 16–19 plasma samples per volunteer were collected from 0.5 up to 72 h post-dose. The popPK was built and post hoc estimates were compared with previously published PK parameters evaluated by non-compartmental analysis in the same cohort. The predictivity of the model for data collected from 40 patients with gastrointestinal stromal tumors at steady state was evaluated.ResultsThe popPK was best described by a two-compartment transit model with first-order elimination. No significant covariates were identified, probably due to the small cohort and the narrow range of demographic covariates; CYP3A5 phenotypes appeared to have some influence on the clearance of imatinib. Good agreement between non-compartment and popPK analyses was observed with the differences of the geometric means/ median of PK estimates below 10%. The model indicated lower clearance for patients compared to healthy volunteers (p value < 0.01).ConclusionThe two-compartment transit model adequately describes the absorption and distribution of imatinib in healthy volunteers. For patients, a lower clearance of imatinib compared to healthy volunteer was estimated by the model. The model can be applied for dose individualization based on trough concentrations assuming no significant differences in absorption between patients and healthy volunteers.

This article focuses on using E-Bayesian estimation for the Weibull distribution based on adaptive type-I progressive hybrid censored competing risks (AT-I PHCS). The case of Weibull distribution for the underlying lifetimes is considered assuming a cumulative exposure model. The E-Bayesian estimation is discussed by considering three different prior distributions for the hyper-parameters. The E-Bayesian estimators as well as the corresponding E-mean square errors are obtained by using squared and LINEX loss functions. Some properties of the E-Bayesian estimators are also derived. A simulation study to compare the various estimators and real data application is applied to show the applicability of the different estimators are proposed.

In this paper, we discuss the statistical analysis of a simple step-stress accelerated competing failure model under progressively Type-II censoring. It is assumed that there is more than one cause of failure, and the lifetime of the experimental units at each stress level follows exponential distribution. The distribution functions under different stress levels are connected through the cumulative exposure model. The maximum likelihood, Bayesian, Expected Bayesian, and Hierarchical Bayesian estimations of the model parameters are derived based on the different loss function. Based on Monte Carlo Simulations. We also get the average length and the coverage probability of the 95% confidence intervals and highest posterior density credible intervals of the parameters. From the numerical studies, it can be seen that the proposed Expected Bayesian estimations and Hierarchical Bayesian estimations have better performance in terms of the average estimates and mean squared errors, respectively. Finally, the methods of statistical inference discussed here are illustrated with a numerical example.

The procedure of selecting the values of hyper-parameters for prior distributions in Bayesian estimate has produced many problems and has drawn the attention of many authors, therefore the expected Bayesian (E-Bayesian) estimation method to overcome these problems. These approaches are used based on the step-stress acceleration model under the Exponential Type-I hybrid censored data in this study. The values of the distribution parameters are derived. To compare the E-Bayesian estimates to the other estimates, a comparative study was conducted using the simulation research. Four different loss functions are used to generate the Bayesian and E-Bayesian estimators. In addition, three alternative hyper-parameter distributions were used in E-Bayesian estimation. Finally, a real-world data example is examined for demonstration and comparative purposes.

This paper is concerned with applying the Bayesian and E-Bayesian approaches to estimating the unknown parameters of the modified Topp–Leone–Chen distribution under a progressive Type-II censored sample plan. The paper explores the complexities of different estimating methods and investigates the behavior of the estimates through some computations. The Bayes and E-Bayes estimators are obtained under two distinct loss functions, the balanced squared error loss function, as a symmetric loss function, and the balanced linear exponential loss function, as an asymmetric loss function. The estimators are derived using gamma prior and uniform hyperprior distributions. A numerical illustration is given to examine the theoretical results through using the Metropolis–Hastings algorithm of the Markov chain Monte Carlo method of simulation by the R programming language. Finally, real-life data sets are applied to prove the flexibility and applicability of the model.

In this paper new formulas for E-Bayesian and hierarchical Bayesian estimations of the parameter and reliability of the inverse Weibull distribution are obtained in closed forms. To illustrate the applicability of the obtained results, simulated and real data are used which illustrate that E-Bayesian estimate gives superior performance much better than hierarchical Bayesian for the estimate of the parameter of the inverse Weibull distribution.

Digital tools and services collect a growing amount of log data. In the software development industry, such data are integral and boast valuable information on user and system behaviors with a significant potential of discovering various trends and patterns. In this study, we focus on one of those potential aspects, which is task estimation. In that regard, we perform a case study by analyzing computer recorded activities of employees from a software development company. Specifically, our purpose is to identify the task of each employee. To that end, we build a hierarchical framework with a 2-stage recognition and devise a method relying on Bayesian estimation which accounts for temporal correlation of tasks. After pre-processing, we run the proposed hierarchical scheme to initially distinguish infrequent and frequent tasks. At the second stage, infrequent tasks are discriminated between them such that the task is identified definitively. The higher performance rate of the proposed method makes it favorable against the association rule-based methods and conventional classification algorithms. Moreover, our method offers significant potential to be implemented on similar software engineering problems. Our contributions include a comprehensive evaluation of a Bayesian estimation scheme on real world data and offering reinforcements against several challenges in the data set (samples with different measurement scales, dependence characteristics, imbalance, and with insignificant pieces of information).

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.