Ordering Awad–Varma Entropy and Applications to Some Stochastic Models

We consider a generalization of Awad–Shannon entropy, namely Awad–Varma entropy, introduce a stochastic order on Awad–Varma residual entropy and study some properties of this order, like closure, reversed closure and preservation in some stochastic models (the proportional hazard rate model, the proportional reversed hazard rate model, the proportional odds model and the record values model).

Stochastic comparisons of largest-order statistics for proportional reversed hazard rate model and applications

We investigate stochastic comparisons of parallel systems (corresponding to the largest-order statistics) with respect to the reversed hazard rate and likelihood ratio orders for the proportional reversed hazard rate (PRHR) model. As applications of the main results, we obtain the equivalent characterizations of stochastic comparisons with respect to the reversed hazard rate and likelihood rate orders for the exponentiated generalized gamma and exponentiated Pareto distributions. Our results recover and strengthen some recent results in the literature.

Comparison of two sampling schemes in estimating the stress-strength reliability under the proportional reversed hazard rate model

In this paper, point and interval estimation of stress-strength reliability based on lower record ranked set sampling scheme under the proportional reversed hazard rate model are considered. Maximum likelihood, uniformly minimum variance unbiased, and Bayesian estimators of $\mathcal{R}$ are derived and their performances are compared. Various confidence intervals for the parameter $\mathcal{R}$ are constructed, and compared based on the simulation study. Moreover, the record ranked set sampling scheme is compared with ordinary records in case of interval estimations. Finally, a data set has been analyzed for illustrative purposes.

On Estimation of Reliability Functions using Record values from Proportional Hazard Rate Model

Two measures of reliability functions, namely R(t)=P(X>t) and P=P(X<Y) have been studied based on record values from proportional hazard rate model (PHR) model. For estimation of P, we generalize the results of Basirat et al. (2016) when X and Y belong to different family of distributions from PHR model. Uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and Bayes estimator (BS) are obtained for the powers of the parameter and reliability functions. Simulation studies and a real data example have been presented for illustrative purposes. Asymptotic and exact confidence intervals of the parameters and reliability functions are constructed. Testing procedures are also developed for various hypotheses.