The Kaniadakis Weibull distribution (or κ-Weibull distribution) is a probability distribution arising as a generalization of the Weibull distribution. It is one example of a Kaniadakis κ-distribution. The κ-Weibull distribution has been adopted successfully for describing a wide variety of complex systems in seismology, economy, epidemiology, among many others.

The Kaniadakis κ-Weibull distribution is exhibits power-law right tails, and it has the following probability density function:

valid for ${\displaystyle x\geq 0}$, where ${\displaystyle |\kappa |<1}$ is the entropic index associated with the Kaniadakis entropy, ${\displaystyle \beta >0}$ is the scale parameter, and ${\displaystyle \alpha >0}$ is the shape parameter or Weibull modulus.

The Weibull distribution is recovered as ${\displaystyle \kappa \rightarrow 0.}$

The cumulative distribution function of κ-Weibull distribution is given by

${\displaystyle F_{\kappa }(x)=1-\exp _{\kappa }(-\beta x^{\alpha })}$

valid for ${\displaystyle x\geq 0}$. The cumulative Weibull distribution is recovered in the classical limit ${\displaystyle \kappa \rightarrow 0}$.

The survival distribution function of κ-Weibull distribution is given by