Some Statistics in Polar Coordinate System with Uniform Angles

Abstract

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

Keywords

• Goodness of fit test,Polar distribution,Polar histogram,Random number

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