M.Z. Raqab

Bio: M.Z. Raqab is an academic researcher from University of Jordan. The author has contributed to research in topics: Statistics & Weibull distribution. The author has co-authored 1 publications. Previous affiliations of M.Z. Raqab include King Abdulaziz University.

Estimation of stress-strength reliability R=P(X>Y) based on Weibull record data in the presence of inter-record times

Abstract: A considerable body of literature has been recently devoted to the inference problem of the reliability parameter R = P ( X > Y ) based on record data. In this article, we consider the records as well as the corresponding inter-record times to develop inference procedures for R assuming X and Y come from Weibull distribution. The maximum likelihood estimator of R and its corresponding confidence interval are determined. Bayesian analyses involving Tierney and Kadane’s approximation and Metropolis-Hasting samplers are used to estimate R based on LINEX and square error loss functions. In addition, the estimation problem of R is discussed in the models with known shape parameters. To compare all methods developed here, numerical simulation is carried out. Finally, different real data sets are analyzed.

Estimation of the Kumaraswamy distribution parameters using the E-Bayesian method

Abstract: The Kumaraswamy distribution (KD) is widely applied for modeling data in practical domains, such as medicine, engineering, economics, and physics. The present work proposes the Bayesian estimators of KD parameters through the use of type-II censoring data. Both E-Bayesian and Bayesian estimation approaches are briefly described, along with several loss functions, namely, linex loss function (LLF), weighted linex loss function (WLLF), and composite linex loss function (CLLF). In the Bayesian framework, gamma distribution has been utilized as a conjugate distribution in view of finding theoretical results. The E-Bayesian estimators for the hyperparameter using different distributions are developed. Moreover, a novel loss function referred to as the weighted composite loss function (WCLLF) in the estimation perspective is established. Finally, the Monte Carlo simulation approach is carried out to reveal that the new suggested loss function outperforms several counterparts in determining the shape parameter of the KD.

Statistical inference based on lower record values for the inverse Weibull distribution under the modified loss function

Abstract: The main objective of this article is to develop a linear, exponential loss function (LXLF) to the dependability value and variables of the Inverse Weibull Distribution (IWD) according to Lowest Record Values. By weighting the LXLF to construct current function loss, the modified linear, exponential loss function (WLXLF) was named. Then use WLXLF to estimate the parameters and reliability functions of the (IWD). After that, we evaluated how well the prediction made in this article performed against the Bayesian estimator using the symmetric and asymmetric loss functions and maximum likelihood estimation (MLE). The credibility range for the values of the parameters and durability function has been created using the parametric bootstrap approach, and the outcomes have been contrasted via a Monte Carlo simulation. An actual data set from a realistic situation was utilized to explain the concept. The computer simulation results demonstrated that the suggested method, performed as expected, was the best for estimating the scale parameter and reliability function. The proposed technique performed well in estimating the shape parameter based on real data and had an acceptable performance for estimating scale parameters and reliability functions.

Estimation of stress-strength reliability from unit-Burr Ⅲ distribution under records data

Abstract: This paper explores estimation of stress-strength reliability based on upper record values. When the strength and stress variables follow unit-Burr Ⅲ distributions, a generalized inferential approach is proposed for estimating stress-strength reliability (SSR). Under the common strength and stress parameter case, two types of pivotal quantities are constructed respectively, and then the generalized point and interval estimates for SSR are proposed in consequence, where the associated Monte-Carlo sampling approach is provided for computation. In addition, when strength and stress variables feature unequal model parameters, different generalized point and confidence interval estimates are also established in this regard. Extensive simulation studies are conducted to examine the behavior of proposed methods. Finally, a real-life data example is presented for illustration.

Estimation of Multicomponent Stress-strength Reliability under Inverse Topp-Leone Distribution

Abstract: In this article, the reliability inference for a multicomponent stress-strength (MSS) model, when both stress and strength random variables follow inverse Topp-Leone distributions, was studied. The maximum likelihood and uniformly minimum variance unbiased estimates for the reliability of MSS model were obtained explicitly. The exact Bayes estimate of MSS reliability was derived the under squared error loss function. Also, the Bayes estimate was obtained using the Monte Carlo Markov Chain method for comparison with the aforementioned exact estimate. The asymptotic confidence interval was determined under the expected Fisher information matrix. Furthermore, the highest probability density credible interval was established through using Gibbs sampling method. Monte Carlo simulations were implemented to compare the different proposed methods. Finally, a real life example was presented in support of the suggested procedures.