Moments of q-Normal and conditional q-Normal distributions

preprint2015arXivOpen access

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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Moments of q-Normal and conditional q-Normal distributions

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