AI 中文总结
研究基于广义Tsallis熵测度的递增凸序检验，引入相关不完全熵测度及偏序，建立针对有序备择假设的非参数检验，推导渐近性质，通过模拟评估有限样本性能，并与其他检验比较。
AI 中文摘要
本文研究了几种不完全熵测度，即不完全加权累积剩余熵、不完全累积剩余Tsallis熵及其加权版本，并引入了相关的偏序。研究了它们与某些著名随机序的联系。基于这些特征，开发了一类针对有序备择假设的随机相等性的非参数检验。推导了所提检验的渐近性质，并通过在各种备择模型和样本量下的广泛蒙特卡罗模拟评估了它们的有限样本性能。还将这些检验与Zardasht（2015）提出的基于不完全累积剩余熵的检验进行了比较。
英文摘要
In this paper, we study several incomplete entropy measures, namely the Incomplete Weighted Cumulative Residual Entropy, the Incomplete Cumulative Residual Tsallis Entropy and its weighted version, and introduce the associated partial orderings. Their connections with certain well-known stochastic orderings are also investigated. Based on these characterizations, a class of nonparametric tests for stochastic equality against ordered alternatives is developed. The asymptotic properties of the proposed tests are derived, while their finite-sample performances are assessed through extensive Monte Carlo simulations under various alternative models and sample sizes. These tests are further compared with the test based on incomplete cumulative residual entropy proposed by Zardasht (2015).
Comments21 pages, one figure
