Originally proposed by the statisticians George Box and David Cox in 1964,[2] and known as the reverse Box–Cox transformation for

In a similar procedure to how the exponential distribution can be derived (using the standard Boltzmann–Gibbs entropy or Shannon entropy and constraining the domain of the variable to be positive), the q-exponential distribution can be derived from a maximization of the Tsallis Entropy subject to the appropriate constraints.

The Lomax parameters are: As the Lomax distribution is a shifted version of the Pareto distribution, the q-exponential is a shifted reparameterized generalization of the Pareto.

When q > 1, the q-exponential is equivalent to the Pareto shifted to have support starting at zero.

Random deviates can be drawn using inverse transform sampling.

Being a power transform, it is a usual technique in statistics for stabilizing the variance, making the data more normal distribution-like and improving the validity of measures of association such as the Pearson correlation between variables.

[3] It is also found in atomic physics and quantum optics, for example processes of molecular condensate creation via transition through the Feshbach resonance.