Gaussian q-distribution

The Gaussian \( q \)-distribution is a generalization of the traditional Gaussian (normal) distribution that incorporates the concept of non-extensivity and is part of the broader family of distributions used in q-statistics (also known as Tsallis statistics). This distribution arises in contexts where systems exhibit long-range correlations and is used to describe phenomena that cannot be accurately characterized by the standard Gaussian distribution due to the presence of heavy tails or other non-standard features.