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 .
|Date of creation||2013-03-22 14:33:30|
|Last modified on||2013-03-22 14:33:30|
|Last modified by||CWoo (3771)|