Exponential distribution: Difference between revisions
Jump to navigation
Jump to search
imported>Ragnar Schroder (Creating initial stub) |
mNo edit summary |
||
(10 intermediate revisions by 4 users not shown) | |||
Line 1: | Line 1: | ||
The '''[[exponential distribution|exponential distribution]]''' is a class of [[continuous probability distribution|continuous probability distributions]] | {{subpages}} | ||
The '''[[exponential distribution|exponential distribution]]''' is any member of a class of [[continuous probability distribution|continuous probability distributions]] assigning probability | |||
It | : <math>e^{-x/\mu} \,</math> | ||
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. | |||
The exponential distribution is one of the most important elementary distributions. | The exponential distribution is one of the most important elementary distributions. | ||
==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]] P(X>x+ | 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=== | ||
Let X be a real, positive stochastic variable with [[probability density function]] | Let ''X'' be a real, positive stochastic variable with [[probability density function]] | ||
: <math>f(x)= \lambda e^{-\lambda x}\,</math> | |||
for ''x'' ≥ 0. Then ''X'' follows the exponential distribution with parameter <math>\lambda</math>. | |||
==See also== | ==See also== | ||
Line 35: | Line 29: | ||
*[[Poisson distribution]] | *[[Poisson distribution]] | ||
== | ==References== | ||
{{reflist}}[[Category:Suggestion Bot Tag]] | |||
[[Category: |
Latest revision as of 17:00, 14 August 2024
![](http://s9.addthis.com/button1-share.gif)
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 .