### Exponential Distribution

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The exponential distribution is a special case of the Weibull distribution. For exponential distributions, the parameter `beta` is fixed at 1. Exponential distributions are used to model occurrences of events that are independent of the life of the product (i.e., parts that don't wear but suddenly fail). The life of an electronic component is likely to fit an exponential distribution. The density and distribution functions are given by:

`f(x) = 1/alpha e^(-((x-a)/alpha))`

`F(x) = 1-e^(-((x-a)/alpha))`