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Mathematics & Statistics

Colloquia — Summer 2007

Thursday, June 7, 2007

Title
Speaker

Time
Place

Information Volatility
M. Rao
University of Florida
3:00pm-4:00pm
ENG 4
TBA

Abstract

As is well known the Shannon Entropy $$H(X)$$ of a random variable $$X$$ is by definition $$-\int_0^{\infty} f(x)\log f(x)\,dx$$, which is the expectation of the random variable $$-\log f(X)$$. In this talk we study its variance, which we call its Information Volatility (or $$\mathrm{IV}(X)$$ for short). $$\mathrm{IV}(X)$$ has some very good properties not shared by Shannon Entropy. For example, $$\mathrm{IV}(X)$$ equaling zero characterizes the Uniform distribution; $$\mathrm{IV}(X)$$ is invariant under the affine transformation; and has some convergence properties.