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1.
《Journal of Statistical Computation and Simulation》2012,82(12):2688-2699
It has long been known that, for many joint distributions, Kendall's τ and Spearman's ρ have different values, as they measure different aspects of the dependence structure. Although the classical inequalities between Kendall's τ and Spearman's ρ for pairs of random variables are given, the joint distributions which can attain the bounds between Kendall's τ and Spearman's ρ are difficult to find. We use the simulated annealing method to find the bounds for ρ in terms of τ and its corresponding joint distribution which can attain those bounds. Furthermore, using this same method, we find the improved bounds between τ and ρ, which is different from that given by Durbin and Stuart. 相似文献
2.
Timothy C. Brown Donald I. Cartwright G. K. Eagleson 《Australian & New Zealand Journal of Statistics》1986,28(1):89-96
Two characterizations of the uniform distribution on a suitable compact space are proved. These characterizations are applied to a number of particular examples of which the most interesting is the following: if X , Y and Z are independent n-vectors whose components are independent and identically distributed within a vector, then the pairwise independence of the product moment correlation coefficients between X , Y and Z implies that these vectors are normally distributed. 相似文献
3.
本文采用Speannan秩相关法进行分析,研究调查了高职院校学生的寝室人际关系状况。 相似文献
4.
Extremes of nonexchangeability 总被引:2,自引:1,他引:1
Roger B. Nelson 《Statistical Papers》2007,48(2):329-336
Summary For identically distributed random variables X and Y with joint distribution function H, we show that the supremum of |H(x,y)-H(y,x)| is 1/3. Using copulas, we define a measure of nonexchangeability, and study maximally nonexchangeable random variables and
copulas. In particular, we show that maximally nonexchangeable random variables are negatively correlated in the sense of
Spearman's rho.
An erratum to this article is available at . 相似文献
5.
Nathan Mantel 《The American statistician》2013,67(3):225-228
Under proper conditions, two independent tests of the null hypothesis of homogeneity of means are provided by a set of sample averages. One test, with tail probability P 1, relates to the variation between the sample averages, while the other, with tail probability P 2, relates to the concordance of the rankings of the sample averages with the anticipated rankings under an alternative hypothesis. The quantity G = P 1 P 2 is considered as the combined test statistic and, except for the discreteness in the null distribution of P 2, would correspond to the Fisher statistic for combining probabilities. Illustration is made, for the case of four means, on how to get critical values of G or critical values of P 1 for each possible value of P 2, taking discreteness into account. Alternative measures of concordance considered are Spearman's ρ and Kendall's τ. The concept results, in the case of two averages, in assigning two-thirds of the test size to the concordant tail, one-third to the discordant tail. 相似文献
6.
In this paper, a family of copulas with two parameters is proposed and its dependence analysis is performed. The corresponding family of bivariate distributions with specified marginals is constructed. For normal marginals, the new distributions are non-elliptical and can be applied in data analysis. They provide various alternative hypotheses for testing normality. Finally, an example is given. 相似文献
7.
《Journal of Statistical Computation and Simulation》2012,82(10):2214-2232
The balanced iterative reducing and clustering hierarchies (BIRCH) algorithm handles massive datasets by reading the data file only once, clustering the data as it is read, and retaining only a few clustering features to summarize the data read so far. Using BIRCH allows to analyse datasets that are too large to fit in the computer main memory. We propose estimates of Spearman's ρ and Kendall's τ that are calculated from a BIRCH output and assess their performance through Monte Carlo studies. The numerical results show that the BIRCH-based estimates can achieve the same efficiency as the usual estimates of ρ and τ while using only a fraction of the memory otherwise required. 相似文献
8.
A NEW PROCEDURE FOR ASSESSING LARGE SETS OF CORRELATIONS 总被引:1,自引:0,他引:1
In this paper, a new test of the hypothesis that all the correlations between a set of variables are zero is proposed. It is based on the asymptotic behaviour of the largest of the observed correlation coefficients. Here “asymptotic” refers to the size of the correlation matrix considered. Simulations show that the critical levels, calculated using the asymptotic theory, are conservative but quite accurate, even for small correlation matrices. 相似文献
9.
Short analytical proofs are given for classical inequalities due to Daniels [1950. Rank correlation and population models. J. Roy. Statist. Soc. Ser. B 12, 171–181; 1951. Note on Durbin and Stuart's formula for E(rs). J. Roy. Statist. Soc. Ser. B 13, 310] and Durbin and Stuart [1951. Inversions and rank correlation coefficients. J. Roy. Statist. Soc. Ser. B 13, 303–309] relating Spearman's ρ and Kendall's τ. 相似文献
10.
David C. Blest 《Australian & New Zealand Journal of Statistics》2000,42(1):101-111
Within the bounds of a general theory of rank correlation two particular measures have been adopted widely: Spearman7apos;s rank correlation coefficient, ρ in which ranks replace variates in Pearson's product-moment correlation calculation; and Kendall's τ in which the disarray of x -ordered data due to a y -ordering is measured by counting the minimum number, s ; of transpositions (interchanges between adjacent ranks) of the y -ordering sufficient to recover the x-ordering. Based on insights from the calculation of Kendall's coefficient, this paper develops a graphical approach which leads to a new rank correlation coefficient akin to that of Spearman. This measure appears to stand outside general theorybut has greater power of discrimination amongst differing reorderings of the data whilst simultaneously being strongly correlated with both ρ and τ. The development is focused on situations where agreement over ordering is more important for top place getters than for those lower down the order as, for example, in subjectively judged Olympic events such as ice skating. The basic properties of the proposed coefficient are identified. 相似文献