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• W2159790837 abstract "Let T be a stopping time associated with a sequence of independent random variables Z1;Z2;::: . By applying a suitable change in the probability measure we present relations between the moment or probability generating functions of the stopping time T and the stopped sum ST = Z1 +Z2 +::: +ZT . These relations imply that, when the distribution of ST is known, then the distribution of T is also known and vice versa. Applications are oered in order to illustrate the applicability of the main results, which also have independent interest. In the rst one we consider a random walk with exponentially distributed up and down steps and derive the distribution of its rst exit time from an interval ( a;b): In the second application we consider a series of samples from a manufacturing process and we let Zi;i 1, denoting the number of non-conforming products in the i-th sample. We derive the joint distribution of the random vector (T;ST ), where T is the waiting time until the sampling level of the inspection changes based on a k-run switching rule. Finally, we demonstrate how the joint distribution of (T;ST ) can be used for the estimation of the probability p of an item being defective, by employing an EM algorithm." @default.
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• W2159790837 date "2011-01-01" @default.
• W2159790837 modified "2023-09-27" @default.
• W2159790837 title "On the relation between the distributions of stopping time and stopped sum with applications" @default.
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