Weibull distribution

Commonly used to model time-to-failure data. For example, a manufacturer is interested in calculating the probability that a part fails after one, two, or more years. It has wide application in engineering, medical research, finance, and climatology.

Weibull distribution is described by the shape, scale, and threshold parameters. The case when the threshold parameter is zero is called the 2-parameter Weibull distribution. It is defined only for nonnegative variables.

Depending on the values of the parameters, the Weibull distribution can take various shapes.

One of the main advantages of this distribution is that it can take on the characteristics of other types of distribution making it extremely flexible in fitting different kinds of data. For example,

·    The exponential distribution is a special case of Weibull distribution often used to study the scattering of radiation or wind speed.

·    The Weibull distribution is an alternative to the normal distribution in the case of skewed data.

·    If X follows a Weibull distribution, then Ln(X) follows an extreme value distribution. This distribution is used to describe extreme conditions, such as extreme wind-gust, extreme energy during earthquakes, or extreme stress.

When the shape parameter is 2, the Rayleigh distribution can be derived from the Weibull distribution.