신뢰성 해석을 위한 이중 순환 최우량 추정법을 이용한 일반화 파레토 분포 기법

Abstract

In order to estimate the high reliability, it is necessary to deal with the tail part of the cumulative distribution function (CDF) in greater detail compared to an overall CDF. Generalized Pareto distribution (GPD), is a method of modeling tail part of the CDF, is receiving increased research focus to estimate the high reliability. Current researches on GPD focus how to determine the appropriate number of sample points and its parameters. However, when the threshold value of the GPD is estimated incorrectly, even if it is properly estimated its parameters and the number of sample points, there is a problem in that GPD model may be inaccurate. Therefore, in this paper, double loop maximum likelihood estimation (MLE) based GPD method is proposed to improve the accuracy of the tail model. In order to guarantee the accuracy of reliability, the proposed method determines the accurate threshold value through MLE with the overall samples before estimating GPD over the threshold. To validate the accuracy of the proposed method, it is compared with general GPD model with empirical cumulative distribution function (ECDF). tail part of the CDF, is receiving increased research focus to estimate the high reliability. Current researches on GPD focus how to determine the appropriate number of sample points and its parameters. However, when the threshold value of the GPD is estimated incorrectly, even if it is properly estimated its parameters and the number of sample points, there is a problem in that GPD model may be inaccurate. Therefore, in this paper, double loop maximum likelihood estimation (MLE) based GPD method is proposed to improve the accuracy of the tail model. In order to guarantee the accuracy of reliability, the proposed method determines the accurate threshold value through MLE with the overall samples before estimating GPD over the threshold. To validate the accuracy of the proposed method, it is compared with general GPD model with empirical cumulative distribution function (ECDF).