随机变量分布函数类型的判别算法

Criteria Algorithm of Random Variable Distribution Functions Types

熵是信息论中的一个重要概念，在密码学中有着广泛的应用。熵的统计计算是一个很有价值的研究问题，尤其是随机变量函数未知情况下的熵估计问题较难，而这方面的理论与应用研究均不多。利用余昭平先生对Ｓｈａｎｎｏｎ 熵的估计结果和最大熵原理，证明了一个连续概率分布函数是正态型、指数型或均匀型的充要条件，由此得到一个随机变量分布函数类型的判别算法。这些结果对于信息的采集、分类及处理都有较大的指导作用。

Entropy is an important concept on information theory. It has an extensive application in cryptology. Calculating entropy is a valuable problem. Specially, under the condition of unknown random variable distribution functions, estimating entropy is quite difficult. Theory and application studing on this field is very few. By using the estimation results of Shannon entropy and the maximal entropy principles, it is proved that the continuous probability distribution function is a sufficient and necessary condition of the normal, exponential or uniform types. Thus a criteria algorithm of random variable distribution function types is obtained. These results are very important fro information acquisition, classification and processing.