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Probability of ties and Markov property in discrete order statistics
Authors:Pushpa Lata Gupta  Ramesh C. Gupta
Affiliation:University of Meine at Orono, Orono, ME 04469, USA
Abstract:It is well known that, in the continuous case, the probability that two consecutive order statistics are equal to zero, whereas it is not true when the distribution is discrete. It is, perhaps, for this reason that order statistics from discrete distributions has not been investigated in the literature as much as from a continuous distribution. The main purpose of this paper, therefore, is to obtain the probability of ties when the distribution is discrete. Also it is shown that, in the discrete case, the Markov property does not hold good. However, the order statistics from a geometric distribution forms a Markov chain.
Keywords:60J99  62E99  Discrete Order Statistics  Probability of Ties  Markov Property
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