Exponential Distribution
The continuous distribution on with density for .
Definition 4.6 (Exponential Distribution)
An exponential distribution with parameter is a continuous random variable , denoted , with probability density function
Proof of density validity. We have
Tail probabilities
If , then for ,
Continuous analogue of the geometric distribution
Let and discretise time by with . Then, for every ,
so is a geometric random variable with parameter as . Hence converges in distribution to : the exponential distribution is the continuous analogue of the geometric distribution.
Related
Stated in
- Definition 4.6 (Exponential Distribution)§4.3 Exponential Distribution