A Theorem on Rank Orders for Two Censored Samples

Abstract

Let $m$ and $n$ be the sizes, respectively, of two independent random samples both of which may be censored in an arbitrary manner so that $h(1 \leqq h \leqq m)$ and $k(1 \leqq k \leqq n)$ observations, respectively, remain. If arranged in ascending order, the remaining observations can appear in $\binom{h + k}{h}$ possible rank orders. In this paper we prove a theorem which is useful in obtaining the probability associated with any one of these rank orders, provided the two samples are drawn from populations with identical distribution functions.