Distribution of first-exit times for empirical counting and poisson processes with moving boundaries
- 1 January 1993
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics. Stochastic Models
- Vol. 9 (1) , 91-103
- https://doi.org/10.1080/15326349308807255
Abstract
Let be either (i) the empirical counting process of n IID random variables or (ii) a Poisson process. For these two counting processes we derive the exact distribution of the first time t at which where f is an arbitrary continuous increasing function. An expression for the probability that this stopping time is finite is also givenKeywords
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