In various applied areas such as reliability engineering, molecular biology, finance, etc., the measure of uncertainty of a probability distribution plays an important role. In the present work, we consider the estimation of a function of the scale parameter, namely entropy of several exponential distributions with unknown and unequal location parameters with a common scale parameter under a general class of bowl-shaped location invariant loss functions. The inadmissibility of the minimum risk invariant estimator (MRIE) is proved by deriving a non-smooth improved estimator. Also, we have obtained a smooth estimator which improves upon the MRIE. As an application, we have obtained explicit expressions of improved estimators for two special loss functions: squared error loss and linex loss. It is further shown that these estimators can be derived for four important sampling schemes: (i) complete and i.i.d. sample, (ii) record values, (iii) type-II censoring, and (iv) progressive Type-II censoring. Finally, a simulation study was carried out to compare the risk performance of the proposed estimators.
翻译:在可靠性工程、分子生物学、金融等各种应用领域,概率分布的不确定性的度量具有重要作用。在目前的工作中,我们考虑对比例参数的一个函数进行估计,即,在一般的碗形位置无变化损失功能类别下,若干具有通用比例参数的未知和不均等位置参数的指数分布酶,在一般的碗形位置无变化损失功能类别下,具有共同比例参数。通过得出一个非脉冲改进的估测器,可以证明不容许变化估计器(MRIE)的最低风险。此外,我们获得了一个平稳的估测器,该测算器在MRIE上得到了改进。作为应用,我们获得了两个特殊损失函数:平方误差损失和线轴损失的改良估测器的明确表达。还进一步表明,这些估计器可以用于四个重要的取样方案:(一)完整和一.d.抽样,(二)记录值,(三)二类审查,和(四)累进式二审查。最后,进行了模拟研究,以比较拟议的测算器的风险性。