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arXiv · 1506.07970

Moments of q-Normal and conditional q-Normal distributions

Paweł J. Szabłowski
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Abstract

We calculate moments and moment generating functions of two distributions: the so called $q-$Normal and the so called conditional $q-$Normal distributions. These distributions generalize both Normal ($q=1),$ Wigner ($% q=0,$ $q-$Normal) and Kesten-McKay ($q=0,$ conditional $q-$Normal) distributions. As a by product we get asymptotic properties of some expansions in modified Bessel functions.

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Paweł J. Szabłowski. 2015-06-26. Moments of q-Normal and conditional q-Normal distributions. https://doi.org/10.1016/j.spl.2015.06.027

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