This paper is concerned with the estimation of the Weibull generalized exponential distribution (WGED) parameters based on the adaptive Type‐II progressive (ATIIP) censored sample. Maximum likelihood estimation (MLE), maximum product spacing (MPS), and Bayesian estimation based on Markov chain Monte Carlo (MCMC) methods have been determined to find the best estimation method. The Monte Carlo simulation is used to compare the three methods of estimation based on the ATIIP‐censored sample, and also, we made a bootstrap confidence interval estimation. We will analyze data related to the distribution about single carbon fiber and electrical data as real data cases to show how the schemes work in practice.

Statistical distributions play a prominent role for modeling data in applied fields, particularly in actuarial, financial sciences, and risk management fields. Among the statistical distributions, the heavy‐tailed distributions have proven the best choice to use for modeling heavy‐tailed financial data. The actuaries are often in search of such types of distributions to provide the best description of the actuarial and financial data. This study presents a new power transformation to introduce a new family of heavy‐tailed distributions useful for modeling heavy‐tailed financial data. A submodel, namely, heavy‐tailed beta‐power transformed Weibull model is considered to demonstrate the adequacy of the proposed method. Some actuarial measures such as value at risk, tail value at risk, tail variance, and tail variance premium are calculated. A brief simulation study based on these measures is provided. Finally, an application to the insurance loss dataset is analyzed, which revealed that the proposed distribution is a superior model among the competitors and could potentially be very adequate in describing and modeling actuarial and financial data.

In this article, a progressive-stress accelerated life test (ALT) that is based on progressive type-II censoring is studied. The cumulative exposure model is used when the lifetime of test units follows Pareto-IV distribution. Different estimates as the maximum likelihood estimates (MLEs) and Bayes estimates (BEs) for the model parameters are discussed. Bayesian estimates are derived while using the Tierney and Kadane (TK) approximation method and the importance sampling method. The asymptotic and bootstrap confidence intervals (CIs) of the parameters are constructed. A real data set is analyzed in order to clarify the methods proposed through this paper. Two types of the progressive-stress tests, the simple ramp-stress test and multiple ramp-stress test, are compared through the simulation study. Finally, some interesting conclusions are drawn.

A stress-strength reliability model compares the strength and stresses on a certain system; it is used not only primarily in reliability engineering and quality control but also in economics, psychology, and medicine. In this paper, a novel extension of stress-strength models is presented. The mew model is applied under the generalized exponential distribution. The maximum likelihood estimator, asymptotic distribution, and Bayesian estimation are obtained. A comprehensive simulation study along with real data analysis is performed for illustrating the importance of the new stress-strength model.

M. M. Mohie El-Din, S. E. Abu-Youssef, Nahed S. A. Ali, and A. M. Abd El-Raheem. CSAM 2016;23:269-85. https://doi.org/10.5351/CSAM.2016.23.4.269