On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials
2014 ◽
Vol 51
(2)
◽
pp. 483-491
◽
Keyword(s):
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 ST,i be the stopped sum denoting the number of appearances of outcome 'i' in X1, …, XT, 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, ST,0, ST,1, …, ST,m). Two applications, which have independent interest, are offered to illustrate the applicability and the usefulness of the main results.
Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory
2005 ◽
Vol 42
(01)
◽
pp. 153-162
◽
1987 ◽
Vol 24
(01)
◽
pp. 200-214
◽
Keyword(s):
1994 ◽
Vol 31
(04)
◽
pp. 949-957
◽
Keyword(s):