exponential distribution

Exponential

The exponential distribution is usually used to model the length of time between events in a Poisson process.

The density function is a function of one parameter {% \theta %} and is given by

{% f(x) = \theta e^{- \theta x} %}

The cumulative function is given by

{% F(x) = 1 - e^{- \theta x} %}

The moments of the exponential distribution are given by the following.

{% \mathbb{E}(f(x)) = 1/\theta %}

{%\sigma ^2 = 1/\theta^2 %}