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Most of the characterizations of probability distributions are based onproperties of functions of possibly independent random variables. Weinvestigate characterizations of probability distributions through propertiesof minima or maxima of max-independent, min-independent and quasi-independentrandom variables generalizing the results from independent random variables ofKotlarski (1978), Prakasa Rao (1992) and Klebanov (1973).

On some characterizations of probability distributions based on maxima or minima of some families of dependent random variables