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

Buğra Kaan Tiryaki; Orhan Kesemen

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

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.

Keywords

Bivariate distribution function,Piecewise probability density function; Non-uniform random number generation; Rejection method; Inversion method

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Details

Primary Language

Turkish

Subjects

-

Journal Section

-

Authors

Buğra Kaan Tiryaki

Orhan Kesemen

Publication Date

August 15, 2018

Submission Date

July 10, 2017

Acceptance Date

-

Published in Issue

Year 2018 Volume: 22 Number: 2

IZ

https://izlik.org/JA82YD92ZG

Cite

RIS / Bibtex

APA

Tiryaki, B. K., & Kesemen, O. (2018). Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22(2), 443-457. https://izlik.org/JA82YD92ZG

AMA

1.Tiryaki BK, Kesemen O. Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area. J. Nat. Appl. Sci. 2018;22(2):443-457. https://izlik.org/JA82YD92ZG

Chicago

Tiryaki, Buğra Kaan, and Orhan Kesemen. 2018. “Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (2): 443-57. https://izlik.org/JA82YD92ZG.

EndNote

Tiryaki BK, Kesemen O (August 1, 2018) Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 2 443–457.

IEEE

[1]B. K. Tiryaki and O. Kesemen, “Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area”, J. Nat. Appl. Sci., vol. 22, no. 2, pp. 443–457, Aug. 2018, [Online]. Available: https://izlik.org/JA82YD92ZG

ISNAD

Tiryaki, Buğra Kaan - Kesemen, Orhan. “Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22/2 (August 1, 2018): 443-457. https://izlik.org/JA82YD92ZG.

JAMA

1.Tiryaki BK, Kesemen O. Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area. J. Nat. Appl. Sci. 2018;22:443–457.

MLA

Tiryaki, Buğra Kaan, and Orhan Kesemen. “Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, no. 2, Aug. 2018, pp. 443-57, https://izlik.org/JA82YD92ZG.

Vancouver

1.Buğra Kaan Tiryaki, Orhan Kesemen. Non-Uniform Random Number Generation from Arbitrary Bivariate Distribution in Polygonal Area. J. Nat. Appl. Sci. [Internet]. 2018 Aug. 1;22(2):443-57. Available from: https://izlik.org/JA82YD92ZG