Exponential distribution: Difference between revisions
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imported>Aleksander Stos m (cz live) |
imported>Michael Hardy No edit summary |
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: <math>e^{-x/\mu} \,</math> | : <math>e^{-x/\mu} \,</math> | ||
to the interval <nowiki>[</nowiki>''x'', ∞<nowiki>)</nowiki>. | to the interval <nowiki>[</nowiki>''x'', ∞<nowiki>)</nowiki>, for ''x'' ≥ 0. | ||
It is well suited to model lifetimes of things that don't "wear out", among other things. | It is well suited to model lifetimes of things that don't "wear out", among other things. | ||
Revision as of 15:07, 11 September 2007
The exponential distribution is any member of a class of continuous probability distributions assigning probability
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
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
Let X be a real, positive stochastic variable with probability density function
for x ≥ 0. Then X follows the exponential distribution with parameter .
