On Some Characterizations of Probability Distributions Based on Maxima or Minima of Some Families of Dependent Random Variables

Most of the characterizations of probability distributions are based on properties of functions of possibly independent random variables. We investigate characterizations of probability distributions through properties of minima or maxima of max-independent, min-independent and quasi-independent random variables generalizing the results from independent random variables of Kotlarski (Aequ Math 17:77–82, 1978), Prakasa Rao (Identifiability in stochastic models: characterization of probability distributions, Academic Press, New York, 1992) and Klebanov (Math Notes 13:71–72, 1973).