Llyr Jones is a Developer and Mathematical Analyst for Grid-Tools. He is a Maths graduate from St Andrews University and is currently specializing in data trend analysis for Datamaker™.
This is a family of 2-parameter distributions which are used to model many different phenomena. They are characterised by two positive parameters: a scale parameter λ and a shape parameter k. The Weibull distribution can be thought of as a generalisation of the exponential distribution (when k = 1 it represents an exponential distribution with intensity (1 / λ)) and the Rayleigh distribution (when k = 2).
The primary usage of this distribution is in reliability modeling, where there are sound mechanical grounds behind its usage. In fact, it is suitable for modeling any phenomenon which involves a ‘time to failure’ and the failure rate is proportional to a power of time – in this case the parameter k describes how the failure rate changes over time, as follows:
The Weibull distribution has the following probability density function (when x ≥ 0):
In addition to reliability modeling, the Weibull distribution arises in the following contexts: