Shi Xiaolin, Shi Yimin, Zhou Kuang
School of Electronics Engineering, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.
School of Mathematics and Statistics, Northwestern Polytechnical University, Xi'an 710072, China.
Entropy (Basel). 2021 Feb 8;23(2):206. doi: 10.3390/e23020206.
Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton-Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley's approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.
熵衡量与随机变量相关的不确定性。它在控制论、概率论、天体物理学、生命科学等领域有重要应用。最近，许多作者专注于用不同的寿命分布来估计熵。然而，广义比拉尔（GB）分布的熵估计尚未涉及。在本文中，我们基于自适应II型渐进混合删失数据考虑GB分布的熵和参数估计。使用牛顿 - 拉夫森迭代法获得熵和参数的最大似然估计。借助林德利近似提供不同损失函数下的贝叶斯估计。分别使用德尔塔法和马尔可夫链蒙特卡罗（MCMC）方法获得参数和熵的近似置信区间和贝叶斯可信区间。进行蒙特卡罗模拟研究以观察不同点估计和区间估计的性能。最后，为说明目的分析了一个真实数据集。
