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Marginal distributions of the counting process associated with generalized order statistics. (English) Zbl 1167.62047

Summary: By using results from the distribution theory of generalized order statistics, the finite dimensional marginal distributions of the associated counting process are derived in terms of Meijer’s \(G\)-functions. Moreover, some properties of the corresponding transition probabilities are given. The results are obtained by using a new representation of the cumulative distribution function of a single generalized order statistic in terms of the \(G\)-function. As an application, a Bayes estimator based on observations of the counting process of generalized order statistics from a one-parameter exponential distribution is determined.

MSC:

62G30 Order statistics; empirical distribution functions
33C90 Applications of hypergeometric functions
62M99 Inference from stochastic processes
60E05 Probability distributions: general theory
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References:

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