Moments of q-Normal and conditional q-Normal distributions

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 ( $q-$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.

References in corpus (1)

• Random matrices, non-backtracking walks, and orthogonal polynomials

Cited by in corpus (3)

• Statistical Nuclear Spectroscopy with $q$-normal and bivariate $q$-normal distributions and $q$-Hermite polynomials
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions
• Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths