Exponential distribution

The exponential distribution is any member of a class of continuous probability distributions assigning probability

$e^{-x/\mu }\,$

to the interval [x, ∞).

It is well suited to model lifetimes of things that don't "wear out", among other things.

The exponential distribution is one of the most important elementary distributions.

A basic introduction to the concept

The main and unique characteristic of the exponential distribution is that the conditional probabilities P(X > x + 1) stay constant for all values of x.

More generally, we have P(X > x + s | X > x) = P(X > s) for all x, s ≥ 0.

Formal definition

Let X be a real, positive stochastic variable with probability density function

$f(x)=\lambda e^{-\lambda x}{\mbox{ for }}x>0.$

Then X follows the exponential distribution with parameter $\lambda$.

See also

• Continuous probability distribution
• Probability
• Probability theory

Related topics

• Poisson distribution