Some Statistics in Polar Coordinate System with Uniform Angles

Abstract

In this study, some bivariate distribution functions are defined in the polar coordinate system andrandom numbers are generated from these distribution functions. In these definitions, the angularchange of the probability density function is taken as constant, and the distance change isperformed based on the univariate probability density function. Also, the chi-square goodnessof-fit test is proposed for random numbers generated in the polar coordinates. Four differentdistribution functions are selected to evaluate the success of the proposed chi-square goodness offit test for polar distribution functions. Lastly, the validity and the success of the proposed methodis shown in the simulation study and the real-life example.