On the Joint Distribution of Stopping Times and Stopped Sums in Multistate Exchangeable Trials
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 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.
2014 ◽
Vol 51
(2)
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pp. 483-491
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Asymptotic Probabilities of an Exceedance Over Renewal Thresholds with an Application to Risk Theory
2005 ◽
Vol 42
(01)
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pp. 153-162
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1987 ◽
Vol 24
(01)
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pp. 200-214
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Keyword(s):
1994 ◽
Vol 31
(04)
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pp. 949-957
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Keyword(s):