Conditional Stochastic Ordering And Entropy Ordering

In recent years, the stochastic ordering has been a extensive research conclusions, it has a wide range of applications in the field of financial mathematics, communication systems, queuing theory, system reliability, management science and so on. But in reality problems, stochastic ordering model often using a conditional distribution to characterize. Therefore, the study of conditional stochastic ordering and the relations between its and entropy ordering have important theoretical background and practical value.Sochastic ordering is a portrait of an ordering relations between the random variables, entropy ordering is a new stochastic ordering. This paper mainly discuss that when the parameters of a random variable is a random variable, wherther or not the random variable have the parameter ordering. Based on the study of the relations between stochastic order and entropy ordering, combined with the meaning and motivation, we explore the conditional stochastic ordering, and obtain the conclusion of the conditional stochastic order and the relations between its and entropy ordering.The content of this paper is divided into four parts. Firstly, we briefly review the background of stochastic ordering, and then a brief introduction to the definition of some stochastic orderings, Shannon entropy and relative entropy. In chapter2, we define a conditional binomial distribution, abtain some properties, such as the mathematical expectation, variance, characteristic function and so on. We also discuss the relations between the conditional stochastic order and entropy order. In chapter3and4, we promot the theory to the conditional Poisson distribution and the conditional normal distribution, we also get the similar conclusions. Finally, a summary of the full text.