Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.
Relations for the marginal, joint, conditional characteristic functions of k-th upper and lower record values from generalized Pareto distribution and inverse generalized Pareto distribution are given.
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Bayesian estimation for the two parameters of a Gumbel distribution are obtained based on kth lower record values. Prediction, either point or interval, for future kth lower record values is also presented from a Bayesian view point. Some of the results of [4] can be obtained as special cases of our results (k=1).
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Using characterization conditions of continuous distributions in terms of moments of order statistics given in [12], [23], [6] and [7] we present new goodness-of-fit techniques.
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The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on m selected kth record values are presented for the parameters of the Gumbel and Burr distributions.