order statistics
Let be random variables with realizations in . Given an outcome , order in non-decreasing order so that
Note that and . Then each , such that , is a random variable. Statistics defined by are called order statistics of . If all the orderings are strict, then are the order statistics of . Furthermore, each is called the th order statistic of .
Remark. If are iid as with probability density function (assuming is a continuous random variable), Let Z be the vector of the order statistics (with strict orderings), then one can show that the joint probability density function of the order statistics is:
where and .
Title | order statistics |
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Canonical name | OrderStatistics |
Date of creation | 2013-03-22 14:33:30 |
Last modified on | 2013-03-22 14:33:30 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 8 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 62G30 |