A random variable, X, that has a Weibull distribution can take any positive value and has probability density function f, given bywhere c is a positive constant. The distribution has mean and variance , where Γ is the gamma function. The Weibull distribution has been found to be very useful for describing the distribution of the lifetimes of components and for analysing meteorological data—particularly in the context of extreme events.

Weibull distribution. The shape depends on the parameter c. With c < 1 the distribution is often used to model extreme lifetimes.