To understand what makes the ranked set sample (RSS) different from a simple
random sample (SRS) of the same size, we consider the simple case of a single cycle (m
7
= 1) with set size k and perfect judgement ranking. In this case, the ranked set sample
observations are also the respective order statistics. Let X1, …, Xk denote a simple
random sample of size k from a continuous population with p.d.f. f(x) and c.d.f. F(x)
and let X be a ranked set sample of size k obtained as described in Section 2 from
k independent random samples of k units each.