Abstract
A new approach to theory of continuous probability distributions, based on scalar-valued score functions, offers the score mean as a finite typical value of distributions including the heavy-tailed ones. In the article, we define the score variance as a finite measure of variability of distributions with respect to the typical value and discuss its properties and methods of its estimation. By means of the square root of the score variance we introduce a generalized Rao distance in the sample space.
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