Estimating the probability of winning (losing) in a gambler's ruin problem with applications |
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Authors: | Ramesh C. Gupta |
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Affiliation: | University of Maine at Orono, Orono, ME 04469, USA |
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Abstract: | In a classical gambler's ruin problem, the distribution of the number of games lost till ruin is considered, which we call the lost game distribution (LGD). Some applications of LGD in the theory of queues, in the theory of epidemic and in certain clustering and branching models are mentioned. The maximum likelihood estimation of LGD in the framework of modified power series distribution (MPSD), introduced by the author (1974), is studied. The variance and bias of the MLE are given and the actual mean of the MLE is obtained by discussing the negative moments of the MPSD in general. The minimum variance unbiased estimator of θk (k≥1) is obtained employing the technique developed by the author (1977) for the class of MPSD. |
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Keywords: | 62E 62F Lost game distribution Modifiied power series distribution Maximum likelihood estimation Minimum variance unbiased estimation Negative moments Bias |
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