Indexes Improvement And Spread Of Dependence Measurement

In light of complexity of correlations between random variables in probability theory and statistics, it is invariably postulated that random variables are independent from one another. Nevertheless, in practice absolute independence is hard to be satisfied. Moreover, the conclusion we reach, after ignoring dependence of random variables, can not conform to the fact The paper improves the measurement which depict the concordance from the dependence among the random variables. The improvement take advantage of concordance measurement, and develop the research of concordance among the random variable.The paper perfects three improvement of concordant measurement. In 2 section, Kendall's x of three-demensional random variables is depicted, accordanting to the geometrical concept of it. Some deep study is made with instrument 'Copula' and arrives at some significant conclusions. It is compared with the property of Kendall's Ï„ of two-demensional random variables and get some sameness and difference between them. The relationship is also built up which is between Kendall's Ï„ of three-demensional random variables and its marginal Kendall's Ï„ of two-demensional random variables.In 3 section, the concept minusconcordance is advanced and its character is explored here. What is more, dependence of minusconcordance, minus quadrant and Kendall's r of three-demensional random variables is discussed. These advantages enrich the concordant theory.Last Kendall's Ï„ rarely gives us a clear idea about concordance of planar random variables. So the paper perfects the definition, brings forward a new concept, namely concordance function, a series of characters and conclusions are reached which is studied with Copula. These show advantages of new definition over original one. Meanwhile, some concrete examples are provided to figure out the result of concordance function and observe its characters.