Abstract
Recurrence relations and identities are often helpful to determine moments of order statistics. In comparison with direct computations via explicit expressions the application may lead to a reduced numerical effort and to a raised accuracy. Thus in the literature we find a lot of results for specific distributions, which are reviewed and developed in Balakrishnan et al. (1988); we also refer to Khan et al. (1983) in case of truncated distributions. Lin (1988) observes that there are similar recurrence relations for exponential, uniform, Pareto and logistic distributions, namely identities for the difference of moments of successive order statistics, and finds them to be characteristic properties. In Kamps (1991) a recurrence relation of this type and a characterization result are given for a class of probability distributions, so that some isolated identities are subsumed, and new ones are found. Such an approach yields recurrence relations valid for distributions with at least two parameters, and moments of non-integral orders; furthermore it provides structural properties and relationships of several probability distributions. In this paper the class of distributions is generalized, including power function, Pareto, Weibull, Burr XII and logistic distributions, and an analogous result for k-th record values is stated.
Published Version
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