İki Bağımsız Log-Normal Dağıtılmış Rastgele Değişkenin Toplamının Logaritması Olan Rastgele Değişkenin Parametrelerinin Hızlı Hesaplanması

Year 2022, Volume: 37 Issue: 1, 261 - 270, 29.03.2022

Zekeriya Tüfekci , Gökay Dişken

https://doi.org/10.21605/cukurovaumfd.1095081

Abstract

Bu çalışmada, iki log-normal dağılımlı rasgele değişkenin logaritması olan rasgele değişkenin ortalama ve varyansını hesaplamak için iki hızlı metot sunulmuştur. Ortalama ve varyansın sadece bir boyutlu nümerik integral metodu ile hesaplanabileceği gösterilmiştir. Önerilen algoritmanın hızı temel algoritmanın hızı ile karşılaştırılmıştır. Benzetim sonuçları önerilen ilk yöntemin çalışma zamanını ortalama %43,98 azalttığını göstermiştir. Benzetim sonuçları ayrıca önerilen ikinci metodun 0,325’ten büyük varyanslar için birinci yöntemden daha hızlı olduğunu göstermiştir..

Keywords

Log-normal dağılımlı rasgele değişkenlerin toplamı, Paralel model kombinasyonu, Nümerik integral, Gürbüzlük

Fast Computation of Parameters of the Random Variable that is Logarithm of Sum of Two Independent Log-normally Distributed Random Variables

Abstract

In this paper, two fast methods are proposed for computation of mean and variance of a random variable which is logarithm of two log-normally distributed random variables. It is shown that mean and variance can be computed using only one dimensional numerical integration method. The speed of the proposedalgorithms is compared with the baseline algorithm. Simulation results showed that the first proposed method decreases the execution time by an average of 43.98 %. Simulation results also showed that the second proposed method is faster than the first proposed method for the variances greater than 0.325.

Keywords

Sum of log-normally distributed random variables, Parallel model combination, Numerical integration, Robustness.

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