Limit laws in the best of 2n - 1 bernoulli trials |
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| Authors: | Richard A Groeneveld Barry C Arnold |
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| Institution: | 1. Statistics Department, Iowa State University, Arnes, Iowa 50011;2. Statistics Department, University of California, Riverside, California 92521 |
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| Abstract: | A series of independent Bernoulli trials is considered in which either an outcome of type A or type B occurs at each trial. The series terminates when n outcomes of one type have occurred. Two observable random variables of interest are the total number of outcomes in the series and the number of outcomes of the “losing kind.” Two methods of approximation of the expectations of these random variables for large n are obtained and compared. The limiting distribution of the number of outcomes of the “losing kind” is considered when a beta distribution is assigned to p. |
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