In this study, we compare two alternative methods to calculate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\hat {\rho }_{\text {\textit {j,k}}}$\end{document}ρ^j,k: the Pearson sample correlation coefficient and the rank correlation coefficient of Kendall’s τ. Kendall and Gibbons [31] have shown the relation between ρ and τ as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\rho= \sin\left(\frac{\pi\tau}{2}\right). $$ \end{document}ρ=sinπτ2.
