The Study And Applicability Involving Dependence Between Random Varieties Based On Copulas

The paper has realized to study on the dependence relations between random variables based on copulas in terms of determining the nature and quantification, resorting to the descripations of dependence properties and association strength. Therefore, broke through the limitation of study with only depending on independence and linear dependence, and broadened the measure range of dependence relations between random variables. Furthermore, the measure precision has been improved wholly and partly, it has demonstrated the developing course of the strength of associate relations by means of numerical value vigorously.The paper is devided into two chapters to study the dependence theory. In the second chapter, first, we began with the dependence informations implied in copula, defined their copulas when the random variables had the most powerful dependence relations. Secondly, the concordance strength has been distinguished and contrasted between different dependence relations, and we have demonstrated the changeable regularity of strength on dependence relations between random variables by means of the change of parameters in Archimedean copulas. Finally, we measured the dependence strength having the aid of the distance between independence and dependence from another angle.Moreover, drawing support from probability integral transforms, we have summarized the character and changeable regularity of the distribution functions of copulas. So it enriched the dependence mechanism. In order to seep copula theory into reliability theory, we defined several new copula classes in the last section.In the third chapter, resorting to the numerical measure, we have main depicted the dependence relations between random variables validly, argued the improvement on depiction dependence made by the concordance measure τ, and analysed it was consistent with correlation coefficient in bivariate exponential distribution; we also summarized comprehensive characters what all sorts of measures possess and mutual relations. In additions, we have illustrated how thetail dependence parameters accompanied with variations of α,β in Archimedeancopulas, so we can obtain the method that we want to find the joint distribution functions given dependence parameters beginning with known joint distribution functions.The ultimate aim of the study of dependence theory is its applications. So in the last chapter, we practiced in reliability theory based on copulas dependence theory; obtained the new produced methods of all sorts of reliability measures in life-span systems which were composed of mutual dependent components, and...