关键词: 随机控制序, 随机序, 混合泊松分布

Abstract: Stochastic dominance ordering, failure-rate ordering and failure-rate function of mixed Poisson distribution are investigated. It is proved that the class of stochastic dominance ordering of mixed Poisson distribution corresponding to the class of structural distribution keeps the stochastic dominance ordering.
However the class of structural distribution corresponding to the class of stochastic dominance order of mixed Poisson distribution is not definitely of stochastic dominance preserving-order. It is shown by examples that the failure function of mixed Poisson random variables does not definitely increase progressively.

Key words: mixed Poisson distribution, stochastic control order, stochastic ordering