based on the point of view of geometrical representation of an intuitionistic fuzzy set, we take into account all three parameters describing intuitionistic fuzzy set, propose a kind of new method to calculate correlation and correlation coefficient of intuitionistic fuzzy sets which is similar to the cosine of the intersectional angle in finite sets and probability space, respectively. further...

Let {X,Xk,i; i ≥ 1, k ≥ 1} be a double array of nondegenerate i.i.d. random variables and let {pn; n ≥ 1} be a sequence of positive integers such that n/pn is bounded away from 0 and ∞. This work is devoted to the solution to an open problem posed in Li, Liu, and Rosalsky (2010) on the asymptotic distribution of the largest entry Ln = max1≤i<j≤pn ∣∣ρ̂(n) i,j ∣∣ of the sample correlation matrix Γ...

We derive sufficient conditions for the cross-correlation coefficient of a multivariate spatial process to vary with location when the spatial model is augmented with nugget effects. The derived class is valid for any choice of covariance functions, and yields substantial flexibility between multiple processes. The key is to identify the cross-correlation coefficient matrix with a contraction m...

where X and Y are random returns. The main innovation introduced by Markowitz is to measure the risk of a portfolio via the joint (multivariate) distribution of returns of all assets. Multivariate distributions are characterized by the statistical (marginal) properties of all component random variables and by their dependence structure. Markowitz described the former by the first two moments of...

In this study, we first build two empirical cross-correlationmatrices in the US stockmarket by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the twomatriceswith the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock m...

In order to undertake controlled investigations into perceptual effects that relate to the interaural cross-correlation coefficient, experiment stimuli that meet a tight set of criteria are required. The requirements of each stimulus are that it is narrow band, normally has a constant cross-correlation coefficient over time, and can be altered to cover the full range of values of cross-correlat...

On the basis of 2200 small (10-100) samples obtained from four random number populations, it is shown that the rank correlation coefficient, p, is 88 adequate a measure of concordance 88 the Pearson product-moment correlation, T. The samples were obtained by using pseudo-random linear and normal number generators for bivariate populations with expected correlation cC'efficientB, r~, of 0.0 and ...