The probability density function of a q-Weibull random variable is:[1] where q < 2,

> 0 are shape parameters and λ > 0 is the scale parameter of the distribution and is the q-exponential[1][2][3] The cumulative distribution function of a q-Weibull random variable is: where The mean of the q-Weibull distribution is where

The expression for the mean is a continuous function of q over the range of definition for which it is finite.

The q-Weibull is a generalization of the Weibull, as it extends this distribution to the cases of finite support (q < 1) and to include heavy-tailed distributions

The q-Weibull is a generalization of the Lomax distribution (Pareto Type II), as it extends this distribution to the cases of finite support and adds the

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