Relation between the Kendall and Spearman coefficients and concordance graphs∗
نویسنده
چکیده
A pair of linear orders L, L′ on an n-element set V is a concordance pair if the Kendall and Spearman correlation measures between L and L′ coincide. A graph is called concordance graph if it has the same number of induced three-vertex one-edged subgraphs as induced three-vertex twoedged subgraphs. It is known (see Fishburn and Monjardet (2000)) that (L, L′) is a concordance pair if and only if the comparability graph of partially ordered set (V, L∩L′) is a concordance graph. In this paper the portion of concordance pairs among all possible pairs of linear orders on V , as well as the portion of concordance graphs among all graphs with vertex set V are estimated. In both cases the answer is O(n−1/3), n →∞. The results were obtained by methods of probability theory.
منابع مشابه
The Spearman and Kendall rank correlation coefficients between intuitionistic fuzzy sets
This paper is a continuation of our previous work on Pearson’s coefficient r and we discuss here the concept of the Spearman correlation coefficient and the Kendall correlation coefficient between Atanassov’s intuitionistic fuzzy sets (A-IFSs, for short) to measure the degree of association between the A-IFSs when the assumption that the data distributions are normal is not valid or when data a...
متن کاملInvestigating the relationship between risk factors and recurrence of urolithiasis in patients referring to health centers in the city of Lar
Introduction & Aim : After urinary tract infections and prostate diseases, urolithiasis are the third cause of referral to urological clinics. The purpose of this study was to investigate the association of urolithiasis with risk factors . Methods & materials : This is a cross-sectional descriptive-analytic study. The sample size was 200 patients and The data collection tool was a questionnair...
متن کاملPreparation of Papers in Two-Column Format for the Proceedings of the 1997 IEEE International Symposium on Electronics and the Environment
The PageRank formula, originally designed for evaluation of significance of web pages, is also usable for evaluation of significance of authors in citation graphs. None of works on this theme takes in notice influence of citation cycles. We are convinced, they should affect the significance of the authors. We used Kendall and Spearman coefficients to evaluate an influence of cycles.
متن کاملOn the comparison of the Spearman and Kendall metrics between linear orders
This paper bears on the comparison of two well-known metrics between linear orders called the Kendall and Spearman metrics or/and of their normalized versions respectively known as the Kendall tau and the Spearman rho. Using a combinatorial approach based on the partial order intersection of the two compared linear orders, we first prove a relation between these two metrics and a semi-metric, e...
متن کاملRelationship between Coefficients of Characteristic Polynomial and Matching Polynomial of Regular Graphs and its Applications
ABSTRACT. Suppose G is a graph, A(G) its adjacency matrix and f(G, x)=x^n+a_(n-1)x^(n-1)+... is the characteristic polynomial of G. The matching polynomial of G is defined as M(G, x) = x^n-m(G,1)x^(n-2) + ... where m(G,k) is the number of k-matchings in G. In this paper, we determine the relationship between 2k-th coefficient of characteristic polynomial, a_(2k), and k-th coefficient of matchin...
متن کامل