New weighted rank correlation coefficients sensitive to agreement on top and bottom rankings

Three new weighted rank correlation coefficients are proposed which are sensitive to both agreement on top and bottom rankings. The first one is based on the weighted rank correlation coefficient proposed by Maturi and Abdelfattah [13 T.A. Maturi and E.H. Abdelfattah, A new weighted rank correlation, J. Math. Stat. 4 (2008), pp. 226–230. doi: 10.3844/jmssp.2008.226.230[Crossref] , [Google Scholar]], the second and the third are based on the order statistics and the quantiles of the Laplace distribution, respectively. The limiting distributions of the new correlation coefficients under the null hypothesis of no association between the rankings are presented, and a summary of the exact and approximate quantiles for these coefficients is provided. A simulation study is performed to compare the performance of Kendall's tau, Spearman's rho, and the new weighted rank correlation coefficients in detecting the agreement on the top and the bottom rankings simultaneously. Finally, examples are given for illustration purposes, including a real data set from financial market indices.