Gaussian q-distribution

In mathematical physics and probability and statistics, the Gaussian q-distribution is a family of probability distributions that includes, as limiting cases, the uniform distribution and the normal (Gaussian) distribution.

[clarification needed] It is a q-analog of the Gaussian or normal distribution.

The probability density function of the Gaussian q-distribution is given by where The q-analogue [t]q of the real number

The cumulative distribution function of the Gaussian q-distribution is given by where the integration symbol denotes the Jackson integral.

The function Gq is given explicitly by where The moments of the Gaussian q-distribution are given by where the symbol [2n − 1]!!