Exponential Distribution:

The exponential distribution is a one-sided distribution completely specified by one parameter r > 0; the density of this distribution is

 

f(x) = ì í î re-rx, x ³ 0 0, x < 0

The mean of the exponential distribution is 1/r.

The exponential distribution is a model for the length of intervals between two consecutive random events in time, or between a given point and the next nearest point. In this case r is the rate of events - that is, the average number of events per a unit interval. (For details on what "random events" means here see Poisson process.

An important property of the exponential distribution is

 

P(x > t+s) = P(x > t) P(x > s).

Because of this property, the exponential distribution is also referred to as a ´memory-less distribution´. One of the applications of the exponential distribution is in queuing theory.

 

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