Exponential distribution

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

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

to the interval [x, ∞), for x ≥ 0.

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[edit]

The main and unique characteristic of the exponential distribution is that the conditional probabilities satisfy P(X > x + s | X > x) = P(X > s) for all x, s ≥ 0.

Formal definition[edit]

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

${\displaystyle f(x)=\lambda e^{-\lambda x}}$

for x ≥ 0. Then X follows the exponential distribution with parameter ${\displaystyle \lambda }$.

See also[edit]

• Continuous probability distribution
• Probability
• Probability theory

Related topics[edit]

• Poisson distribution

References[edit]