Malik Khubiev's Correlation Coefficient: A Robust Sign-Based Measure of Monotonic Relationship

We introduce a new correlation coefficient, denoted as MK, designed to measure the strengthof monotonic relationships between two variables. The proposed coefficient is based entirelyon the signs of successive differences in the dependent variable after sorting by the independent variable. Unlike classical measures such as Pearson’s r, Spearman’s ρ, or Kendall’s τ ,the MK coefficient explicitly incorporates the global trend direction to adjust the contribution of the first observation. This adjustment makes the coefficient highly resistant to outlierswhile maintaining computational simplicity O(n). The MK coefficient ranges from −1 to 1,with extreme values indicating perfect monotonicity. We provide the formal definition, discuss its mathematical properties, derive asymptotic results, and compare its behavior withexisting correlation measures through extensive simulations and a real data example. Bootstrap confidence intervals and permutation tests are provided for inference. The method isparticularly suitable for large datasets containing outliers or measurement errors where quickand robust trend assessment is needed. An R package and Python module are available athttps://github.com/malikkhubiev/mkcorr.