Several Kinds Of Random Sequence Relations And Applications

The nature is the unification of order and disorder. In the point of probability theory, the sequence in the nature is nothing else but may be divided into the inevitable sequence and the stochastic sequence.Inevitable sequence express definite relations, like the size of real number. Then can the indefinite number, namely random variable, compare the size? As a result of its value's randomness, it can't be directly compared on "the size". But studies show that it still might make the quantification comparison under certain mathematics significance. The size of this relationship can use random sequence to describe. How to carry on the random variable comparison under the reasonable significance is the crux of the problem, simultaneously it is also the difficulty of the problem.In recent years, the random sequences are frequently applied in queuing theory, calculation mathematics, computer queuing network, communication systematically, automatic production line system, inventory system, financial insurance domain and so on. Therefore the research of random sequence relations has vital significance and function on practical problems.Combining random sequence of research background and research motivation this paper aims to introduce random sequence of the mathematical theory and its many kinds of applications systematically. Firstly, the article narrates several common kinds of concept about random sequence relationship; Secondly, it briefly introduces the relationship among several random sequences and the random sequences' application in the random optimization, the mathematical statistics, the economics and finance study and so on; Thirdly it calculates the relationship between the Pareto distribution' s random sequence relation and the distribution parameters ,so we can obtain the random sequence relations through the distribution parameters quickly and directly, and also obtains some more detailed stochastic comparison results of a kind of promotion gamma distribution's order statistics; Finally it proposes a comparison of the uncertain variables which is worth further studying.