Definition:Ordered Statistic

Definition

Let $X_1, X_2, X_3, \ldots, X_N$ be a sequence of $N$ independent random variables chosen from an identical probability space.

Let $X_{(1)},X_{(2)},X_{(3)},\ldots,X_{(N)}$ be these measures re-arranged in increasing order.

Then $X_{(i)}$ is said to be the $i$th ordered statistic.