Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area

Orhan Kesemen,Buğra Kaan Ti̇ryaki̇

doi:10.19113/sdufbed.70290

Abstract

Bivariate non-uniform random numbers are usually generated in a rectangular area. However, this is generally not useful in practice because the arbitrary area in real-life is not always a rectangular area. Therefore, the arbitrary area in real-life can be defined as a polygonal approach. Non-uniform random numbers are generated from an arbitrary bivariate distribution within a polygonal area by using the rejection and the inversion methods. Three examples are given for non-uniform random number generation from an arbitrary bivariate distribution function in polygonal areas. In these examples, the non-uniform random number generation is discussed in the triangular area, the Korea mainland and the Australia mainland. The non-uniform random numbers are generated in these areas from the arbitrary probability density function. The observed frequency values are calculated with using both methods in the simulation study and the generated random numbers are tested with the chi-square goodness of fit test to determine whether or not they come from the given distribution. Also, both methods are compared each other with a simulation study.

Highlights

Random number simulations have long been a popular topic in the world of science
The last example, the non-uniform random number generation is performed with the help of the probability density values which are obtained by using the frequencies of the Australian rainforest data
The non-uniform random numbers are generated from an arbitrary bivariate distribution within a polygonal area by using the rejection and the inversion methods

Summary

Introduction

Random number simulations have been studied closely within the areas of mathematics and statistics. Random numbers are used in fields such as communication [1], information and control systems [2], signal processing [3], machine learning [4], biostatistics [5], econometrics [6], mathematical finance [7], biology [8], insurance [9], cryptography [10], simulation [11], computer games [12] and statistical sampling and applications [13]. The rejection method or the inversion method from univariate and bivariate probability density functions are the most commonly used non-uniform random number generation algorithms [11, 14, 15, 16].

Methods

Results

Conclusion