Marginal Distributions of the Counting Process Associated with Generalized Order Statistics
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.