An Estimator of Shannon Entropy of Beta-Generated Distributions and a Goodness-of-Fit Test

The aim of this article is twofold: on the one hand to introduce and study some of the statistical properties of an estimator for the Shannon entropy and on the other hand to develop a goodness-of-fit test for beta-generated distributions and the distribution of order statistics. Beta-generated distributions are a broad class of univariate distributions which has received great attention during the last 15 years, as it obeys nice properties and it extends the distribution of order statistics. The proposed estimator of Shannon entropy of beta-generated distributions is motivated by the respective Vasicek’s estimator, as the latter one is tailored to the class of the beta-generated distributions and the distribution of order statistics. The estimator of Shannon entropy is defined and its consistency is studied. It is, moreover, exploited to build a goodness-of-fit test for the beta-generated distribution and the distribution of order statistics. Simulations are performed to examine the small- and moderate-sample properties of the proposed estimator and to compare the power of the proposed test with the power of competitors under a variety of alternatives.     

球对称静态黑洞熵的计算

用弯曲时空的熵密度对黑洞熵进行了直接计算,避免了求解场方程的困难.由于熵密度在事件视界上是发散的,因此取截断因子来防止发散.结果表明黑洞的量子熵与黑洞表面积成正比.     

Boltzmann方程的意义的探讨

本文试就Boltzmann方程的数学物理内函及其近代物理学的发展,以及为量子力学的建立提供了条件和为统计物理学的发展奠定了基础,从而促使整个物理学的发展进入崭新的革命时期方面来探讨Boltzmann所具有深远意义的物理理论和物理思想,并对Boltzmann方程的意义进行一些粗浅地探讨。     

相对论性理想流体熵密度的计算

求解自引力非辐射体系的熵结构，这个问题很有意义．本文一般地导出相对论性流体热力学第二定律的协变表达式．利用理想流体的熵流守恒和局域能量守恒等基本守恒律推导出熵密度的计算公式．     

EEG的测度熵计算

本文对脑电图(EEG)的测度熵进行数值计算,证实了脑电呈现混沌运动的特征,并发现可以利用EEG的测度熵对人脑功能作定性解释。     

论Schwarzschild黑洞的熵

利用二维球面简并气体模型，证实了Ｓｃｈｗａｒｚｓｃｈｉｌｄ黑洞的熵就是其视界物质的熵．     

熵理思维视角下的科学立法探析

建设法治国家是中国走向现代文明的必然选择,科学立法是法治进程的基础.法律的重要作用在于降低系统不确定性,提高社会有序性.熵是描述、分析和计算系统有序程度的重要而成熟的概念,已在多个学科得到成功应用.在此思维指导下考量中国立法现状,提出四点科学立法建议:简化立法层次,明确立法权限;设立立法配额,推进职业立法;立、改、废、释并举及其常态化;借鉴工程学科成熟的理论和技术,如测试覆盖性分析、风险分析和熵值计算法,形成跨学科的方法.     

Assessment of Resilience to Drought of Rural Communities in Iran

In recent years, drought has inflicted significant damage on agriculture and rural communities in Iran. Resilience is the capability of communities to handle and tolerate exterior pressures such as drought. The purpose of this study was to identify the indicators affecting social resilience against drought, determining the cause of reduction or increase of resilience in different regions. It also focuses on strategies for increasing resilience of rural communities through the provision of social services in Iran. The required information was collected using a questionnaire from five villages, including 237 villagers who were selected through snowball method. Shannon’s entropy and COPRAS methods were employed to determine and classify the drought resilience. The results show that some indicators like modified irrigation methods and new methods of coping with drought have devoted the highest weight. Also, there is a significant relationship between resilience rating of villages with average age of the households and number of households in nonfarm job. Finally, absolute drought resilience of rural communities remained in moderate situation. Doing study in wider areas to coordinate the effective indicators in the matter and studying how empowerment of local communities by providing a variety of social services can be considered as a further research in the future.     

Bootstrap entropy test for general location-scale time series models with heteroscedasticity

This study considers a goodness-of-fit test for location-scale time series models with heteroscedasticity, including a broad class of generalized autoregressive conditional heteroscedastic-type models. In financial time series analysis, the correct identification of model innovations is crucial for further inferences in diverse applications such as risk management analysis. To implement a goodness-of-fit test, we employ the residual-based entropy test generated from the residual empirical process. Since this test often shows size distortions and is affected by parameter estimation, its bootstrap version is considered. It is shown that the bootstrap entropy test is weakly consistent, and thereby its usage is justified. A simulation study and data analysis are conducted by way of an illustration.     

二熵——既是一种完整的宇宙观,又是一种源事理

分析热熵和信熵的科学含义,指出物熵和信熵是宇宙中无时不在、无处不在的两个基本参量。提出包含心熵和社会熵在内的熵的一族。指出通常的四维时空加上物熵维和信熵维所组成的六维时空是熵的世界观的形象表述。提出耗散系统的统一熵流图是源事理分析的基础。