Generalization of the pairwise stochastic precedence order to the sequence of random variables

12/08/2018

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by   Maxim Finkelstein, et al.

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We discuss a new stochastic ordering for the sequence of independent random variables. It generalizes the stochastic precedence order that is defined for two random variables to the case n>2. All conventional stochastic orders are transitive, whereas the stochastic precedence order is not. Therefore, a new approach to compare the sequence of random variables had to be developed that resulted in the notion of the sequential precedence order. A sufficient condition for this order is derived and some examples are considered.