Tu Jiayi, Gui Wenhao
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China.
Entropy (Basel). 2020 Sep 15;22(9):1032. doi: 10.3390/e22091032.
Incomplete data are unavoidable for survival analysis as well as life testing, so more and more researchers are beginning to study censoring data. This paper discusses and considers the estimation of unknown parameters featured by the Kumaraswamy distribution on the condition of generalized progressive hybrid censoring scheme. Estimation of reliability is also considered in this paper. To begin with, the maximum likelihood estimators are derived. In addition, Bayesian estimators under not only symmetric but also asymmetric loss functions, like general entropy, squared error as well as linex loss function, are also offered. Since the Bayesian estimates fail to be of explicit computation, Lindley approximation, as well as the Tierney and Kadane method, is employed to obtain the Bayesian estimates. A simulation research is conducted for the comparison of the effectiveness of the proposed estimators. A real-life example is employed for illustration.
对于生存分析和寿命测试而言，不完整数据是不可避免的，因此越来越多的研究人员开始研究删失数据。本文在广义逐步混合删失方案的条件下，讨论并考虑了具有Kumaraswamy分布特征的未知参数的估计。本文还考虑了可靠性估计。首先，推导了最大似然估计量。此外，还给出了在对称和非对称损失函数（如一般熵、平方误差以及线性指数损失函数）下的贝叶斯估计量。由于贝叶斯估计量无法进行显式计算，因此采用林德利近似以及蒂尔尼和卡丹方法来获得贝叶斯估计量。进行了一项模拟研究，以比较所提出估计量的有效性。采用了一个实际例子进行说明。
