TECHNOLOGY OVERVIEW
# Weibull, Exponential and Rayleigh Distribution

The Weibull distribution is a continuous probability distribution named after the Swedish mathematician Waloddi Weibull

The probability density function for the two parameter Weibull distribution is

where k > 0 is the shape parameter and λ > 0 is the scale parameter of the distribution.

A three parameter Weibull distribution involves allocation parameter, gamma. The pdf is similar to the two parameter pdf with x being replaced by x-gamma.

The Weibull distribution is used extensively in Reliability Analysis

If the quantity X is a "time-to-failure",

A value of k < 1 indicates that the failure rate decreases over time.

A value of k =1 indicates that the failure rate is constant

A value of k > 1 indicates that the failure rate increases over time.

When k=1 the distribution is an Exponential Distribution and when k=2 the distribution is a Rayleigh Distribution

Applications are in Reliability, Survival Analysis, Engineering, Weather Forecasting, Hydrology and others

One application for the Weibull or Rayleigh distribution are used to represent a probabilistic based model to estimate the wind power in a given region.

The exponential distribution is often relevant for applications where the amount of time to some specific event important, such as the next earth quake, or plane crash.

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