independent identically distributed
Two random variables and are said to be identically distributed if they are defined on the same probability space , and the distribution function of and the distribution function of are the same: . When and are identically distributed, we write .
A set of random variables , in some index set , is identically distributed if for every pair .
A collection of random variables () is said to be independent identically distributed, if the ’s are identically distributed, and mutually independent (http://planetmath.org/Independent) (every finite subfamily of is independent). This is often abbreviated as iid.
For example, the interarrival times of a Poisson process of rate are independent and each have an exponential distribution with mean , so the are independent identically distributed random variables.
Many other examples are found in statistics, where individual data points are often assumed to realizations of iid random variables.
Title | independent identically distributed |
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Canonical name | IndependentIdenticallyDistributed |
Date of creation | 2013-03-22 14:27:29 |
Last modified on | 2013-03-22 14:27:29 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 8 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 60-00 |
Synonym | iid |
Synonym | independent and identically distributed |
Defines | identically distributed |