Some improved estimators of the location parameters of several exponential distributions with ordered restriction are derived and compared numerically using Monte Carlo simulations. Note that the two-parameter exponential distribution is very useful in different areas like survival analysis, reliability engineering and biomedical research, where products have a guaranteed failure-free operating time before failures begin to occur. In the present manuscript, we address the component-wise estimation of location parameters of $k~(\ge 2)$ exponential distributions under an asymmetric Linex loss function. The location parameter represents a minimum guaranteed period before failure. At first, we consider the estimation of the location parameters with ordered scale parameters. Next, we address the estimation of ordered location parameters. For this, we take three different cases into account as follows: $(i)$ scale parameters are known, $(ii)$ scale parameters are unknown but equal, $(iii)$ scale parameters are unknown and unequal. In these cases, we establish general inadmissibility results. Further, using the general result, the inadmissibility of the best affine equivariant estimator is proved. The improved estimators are written in explicit forms. Additionally, we show that the results for several important life-testing schemes namely $(i)$ Type-II censoring, $(ii)$ progressive type-II censoring and $(iii)$ record value data can be obtained using i.i.d sample.Finally, for each case, the Monte Carlo simulation technique is used to compare the performance of the proposed estimators based on their risk values. The numerical results reveal a significant improvement of the proposed estimators.

翻译：本文推导了具有序约束的多个指数分布位置参数的若干改进估计量，并通过蒙特卡洛模拟进行了数值比较。需要指出的是，双参数指数分布在生存分析、可靠性工程和生物医学研究等领域具有重要应用价值，这些领域中的产品在失效开始前存在一个保证的无故障运行时间。在本研究中，我们针对非对称线性损失函数下$k~(\ge 2)$个指数分布的位置参数进行分量式估计。位置参数表征失效前的最小保证时间。首先，我们考虑在尺度参数有序情况下的位置参数估计问题。随后，我们研究有序位置参数的估计问题。为此，我们考虑了以下三种不同情形：$(i)$ 尺度参数已知；$(ii)$ 尺度参数未知但相等；$(iii)$ 尺度参数未知且不等。针对这些情形，我们建立了广义不可容许性结果。进一步地，利用该广义结果证明了最佳仿射同变估计量的不可容许性。改进估计量以显式形式给出。此外，我们证明了对于几种重要的寿命试验方案——包括$(i)$ II型截尾、$(ii)$ 渐进II型截尾和$(iii)$ 记录值数据——的相应结果均可通过独立同分布样本获得。最后，针对每种情形，采用蒙特卡洛模拟技术基于风险值比较了所提估计量的性能。数值结果表明所提估计量具有显著改进效果。