Threshold Estimation of Generalized Pareto Distribution Based on Akaike Information Criterion for Accurate Reliability Analysis

In order to perform estimations with 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. The use of a generalized Pareto distribution (GPD) to model the tail part of a CDF is receiving more research attention with the goal of performing estimations with high reliability. Current studies on GPDs focus on ways to determine the appropriate number of sample points and their parameters. However, even if a proper estimation is made, it can be inaccurate as a result of an incorrect threshold value. Therefore, in this paper, a GPD based on the Akaike information criterion (AIC) is proposed to improve the accuracy of the tail model. The proposed method determines an accurate threshold value using the AIC with the overall samples before estimating the GPD over the threshold. To validate the accuracy of the method, its reliability is compared with that obtained using a general GPD model with an empirical CDF.