Topics: Statistics


Let be a random sample. The variables:

…are called order statistics, where is the order statistic of order .

Note that these are just random variables defined as so, nothing more. Once we observe the sample and obtain every realisation , then the order relation of the realisations is used to obtain, in turn, the realisations of the order statistics.



Concerning the density functions of order statistics:

…where and are the density and distribution functions of every (remember that since they’re a random sample, they are iid).