On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials

Abstract

Let T be a stopping time associated with a sequence of independent and identically distributed or exchangeable random variables taking values in {0, 1, 2, …, m}, and let S T,i be the stopped sum denoting the number of appearances of outcome 'i' in X 1, …, X T , 0 ≤ i ≤ m. In this paper we present results revealing that, if the distribution of T is known, then we can also derive the joint distribution of (T, S T,0, S T,1, …, S T,m ). Two applications, which have independent interest, are offered to illustrate the applicability and the usefulness of the main results.