Abstract. There is a connection between the completeness of certain function sequences and the characterizations of the probability distributions. A characterization is a condition involving certain properties of a random variable which identifies the associated probability distribution. In this talk, we give a brief review of the results for complete function sequences. We mention several characterization results based on the moment of the order statistics and record values using the completeness property. Then, we establish some characterization in terms of Fisher information and entropy properties of ordered data.

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