Exponential distribution: Difference between revisions
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imported>Michael Hardy |
imported>Michael Hardy |
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==A basic introduction to the concept== | ==A basic introduction to the concept== | ||
The main and unique characteristic of the exponential distribution is that the [[conditional probability|conditional probabilities]] | The main and unique characteristic of the exponential distribution is that the [[conditional probability|conditional probabilities]] satisfy P(''X'' > ''x'' + ''s'' | ''X'' > ''x'') = P(''X'' > ''s'') for all ''x'', ''s'' ≥ 0. | ||
===Formal definition=== | ===Formal definition=== | ||
Revision as of 19:42, 8 July 2007
The exponential distribution is any member of a class of continuous probability distributions assigning probability
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 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 .
