Application - [A12]

23-11-2022 169 words One minute

Contents

Question

Consider R (radius), A(angle) uniform rv’s and use them as random polar coordinates on a plane. Determine the empirical distribution of the corresponding Cartesian coordinates (X,Y).

Application

The developed application following the homework’s request, shows the intuition behind the Box-Muller method for generating Random Variables with a Normal Distribution. In fact, once the points generated with the polar coordinates are converted to Cartesian coordinates, the resulting distribution is a Normal Distribution. This fact can be easily seen by observing the histogram of the generated points from the point of view of the X and Y axis.

../images/a12.png — Application 12 simulation with 10000 generated points

Library

For this application I used a self-developed library, the code for it can be found on the same Github repository used for the applications. The whole library can also be downloaded as a ZIP file from the Releases section.

Source Code

The application source code can be found on Github and the whole project folder is saved as a ZIP file in this Release