The informational energy of Onicescu is a positive quantity that measures the amount of uncertainty of a random variable. But contrary to Shannon's entropy, the informational energy increases when randomness decreases. We report closed-form formula for Onicescu's informational energy and its associated correlation coefficient when the probability distributions belong to an exponential family. We show how to instantiate the generic formula for several common exponential families.
翻译:Oniicescu的信息能量是一个正数,可以测量随机变量的不确定程度。但是与香农的酶相反,当随机性下降时,信息能量会增加。我们报告Oniicescu的信息能量的闭式公式及其相关相关系数,当概率分布属于指数式家庭时。我们展示了如何对多个常见指数家庭采用通用公式。