On the Gaussian q-Distribution

Details On the Gaussian q-Distribution On the Gaussian q-Distribution

2008-07-11

arxiv.org/abs/0807.1918v4

J. Math. Anal. Appl. 358. (2009) 1-9

Mathematics

Probability

12 pages, 5 figures

Scientific paper

We present a study of the Gaussian q-measure introduced by Diaz and Teruel from a probabilistic and from a combinatorial viewpoint. A main motivation for the introduction of the Gaussian q-measure is that its moments are exactly the q-analogues of the double factorial numbers. We show that the Gaussian q-measure interpolates between the uniform measure on the interval [-1,1] and the Gaussian measure on the real line.

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