Abstract
Tsallis entropy, which is one of nonextensive entropies, gives a q-normal distribution as an equilibrium probability density function. Although a q-normal distribution is popular, there exists a problem what it means by calculating an expectation value with a corresponding escort distribution not a q-normal distribution itself. But we have an amazing property such that an escort distribution obtained by a q-normal distribution with a parameter q and a variance is another q-normal distribution with a different value of q and a scaled variance. Therefore calculating an expectation value with an escort distribution corresponds to calculating the expectation value with another q-normal distribution, that is to say, an escort distribution is nothing but another q-normal distribution. However it still remains the question why an expectation value should be calculated by another q-normal distribution. We call the procedure to get another q-normal distribution from a q-normal distribution through an escort distribution τ-transformation. This τ-transformation keeps a support of a q-normal distribution invariant, and makes the tails of a q-normal distribution thicker/thinner depending on a value of q. Thus a τ-transformation looks like a kind of multiresolutional analysis, if we consider a q-normal distribution as a window function.
Published Version
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