Surface curvature analysis of bivariate normal distribution: A Covid-19 data application on Turkey

Abstract

Principal curvatures have free-form rigid surfaces' invariant features. Therefore they are widely used in several fields for various applications, such as determining the corresponding points between an object and a free-form scene. In this study, the authors analysed the surface curvature of a bivariate normal distribution. A novel approach for classifying bivariate normal surfaces based on curvature statistics concerning correlation structures is presented. The principal curvatures, Gaussian, and mean curvatures were obtained using the data generated from the bivariate normal distribution. The degree of dependency bivariate data directly affects the shape and curvature structures of the bivariate normal distribution surface. Different parameters, from uncorrelated to highly correlated variables, for the correlation of the bivariate normal distribution based on the data have been examined. The effects of the correlation on the distribution surface characteristics have been analysed individually and collectively. This study presents theoretical results in addition to the results of the simulation and real datasets. The simulation data presents the relationship between the independence of the variables and the uniformity of the kappa(n2) values. The other application is based on the curvature properties of the bivariate normal surface on Covid-19 as real data.