Orhan KESEMEN, Buğra Kaan TİRYAKİ

Çokgensel Bölgede Keyfi İki Değişkenli Dağılımdan Düzgün Olmayan Rastgele Sayı Üretimi

İki değişkenli bir uzayda rastgele sayılar genellikle dikdörtgensel bir alan içerisinde üretilmektedir. Ancak uygulamalarda her zaman dikdörtgensel bir alan olamayacağı için keyfi bir alan, çokgensel bir yaklaşım kullanılarak tanımlanmaya çalışılmıştır. Çokgensel bir alan içindeki keyfi iki değişkenli dağılımdan düzgün olmayan rastgele sayılar ret ve ters yöntemleri kullanarak üretilmiştir. Çokgensel alanlardaki keyfi iki değişkenli dağılım fonksiyonundan düzgün olmayan rastgele sayı üretimi için üç ayrı örnek verilmiştir. Bu örneklerde, düzgün olmayan rastgele sayılar üçgen alanında, Kore anakarasında ve Avustralya anakarasında üretilmiştir. Düzgün olmayan rastgele sayılar bu alanlarda keyfi olasılık yoğunluk fonksiyonundan üretilmiştir. Gözlenen frekans değerleri, simülasyon çalışmasında her iki yöntem kullanılarak hesaplanmıştır ve üretilen rastgele sayıların verilen dağılımdan gelip gelmediklerini belirlemek için ki-kare uyum iyiliği testi kullanılmıştır. Ayrıca, her iki yöntem bir simülasyon çalışması ile birbirleriyle karşılaştırılmıştır.

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

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

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