Order statistics¶
Takes n random variables $\(X_1, X_2, \cdots, X_n\)$
now we transform the random variables such that
\[X_{(1)}, X_{(2)}, \cdots , X_{(n)}\]
Satisfy:
\[X_{(1)} \le X_{(2)} \le \cdots \le X_{(n)}\]
The transformed random variables \(X_{(.)}\) are called order statistics.
And are useful to determine extremes (min, max) or quantiles.