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