Research Of Tsallis Survival Entropy Theory

Entropy was first introduced by German physicist R. Clausius in the rmodynamics, subsequently its definition and application was widely expanded in other domains. The Shannon entropy is a central concept in the information theory, it was first advanced in the well-known "The Mathmatical Theory of Communication" paper by Shannon in 1948. After Shannon entropy was advanced; it was immediately adopted by engineers and mathematicians all over the world. Everybody studies, expands and consummates it in detail, so this discipline is immediately prosperous. But after scholars of all over the world made carefully discuss and research in the Shannon entropy, they discovered it also has some defect and insufficiency, so many scholars continually expanded and consummated it. Compared to the density function, defining the entropy with the survival function in the theory has a broader applicable scope, so one of the important thought is defining the entropy with the survival function. M. Rao, and F. Wang et al. creatively proposed Cumulative Residual Entropy(CRE) in 2003, and Konstantinos Zografos and Saralees Nadarajah proposed the survival exponential entropy and the generalized survival exponential entropy in 2004, and has conducted thorough extensive research to its nature.This paper was inspirited by CRE and the survival exponential entropy. Firstly, we used the survival function to give the definition of a kind of new entropy measure -Tsallis Survival Entropy on the Tsallis entropy foundation, which we considered as the survival function edition. In the following we had studied its some basic properties and gave the definitions of correlation conditions, such as: Conditional Tsallis Survival Entropy , mutual information and so on, and discussed their correlation properties. Finally, we inferred the expressions for Tsallis Survival Entropy of some continuous distributions, made a brief summary on the relations of several kinds of entropies which were involved to this paper, and obtained some important conclusions.