多个指数分布总体的Tsallis熵估计
Estimation of Tsallis entropy for exponentially distributed several populations
AI总结：
本文研究多个指数分布总体的Tsallis熵估计，提出Stein型改进估计和基于Brewster技术的光滑估计以降低风险，并给出贝叶斯估计及数值模拟验证。
摘要：
我们研究了有限个独立总体的Tsallis熵估计问题，其中每个总体在q>0时服从具有相同尺度参数和不同位置参数的指数分布。我们推导出一种Stein型改进估计，证明了参数函数的最佳仿射等变估计是不可容许的。利用Brewster技术得到了一类光滑估计，使风险值得到显著改善。我们计算了一个和两个总体的Brewster-Zidek估计，以说明与最佳仿射等变估计和Stein型估计的比较。我们进一步推导出采用逆伽马先验的贝叶斯估计，该估计以最佳仿射等变估计作为特例。我们利用单个总体的模拟样本提供了数值说明，目的是展示样本量、位置参数和熵指数对估计的影响。
英文摘要：
We study the estimation of Tsallis entropy of a finite number of independent populations, each following an exponential distribution with the same scale parameter and distinct location parameters for $q>0$. We derive a Stein-type improved estimate, establishing the inadmissibility of the best affine equivariant estimate of the parameter function. A class of smooth estimates utilizing the Brewster technique is obtained, resulting in a significant improvement in the risk value. We computed the Brewster-Zidek estimates for both one and two populations, to illustrate the comparison with best affine equivariant and Stein-type estimates. We further derive that the Bayesian estimate, employing an inverse gamma prior, which takes the best affine equivariant estimate as a particular case. We provide a numerical illustration utilizing simulated samples for a single population. The purpose is to demonstrate the impact of sample size, location parameter, and entropic index on the estimates.
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