Abstract

We investigate point estimation and confidence interval estimation for the heavy-tailed generalized Pareto distribution (GPD) based on the upper record values. When the shape parameter is known, the bias-corrected moments estimators and maximum likelihood estimators (MLE) for the location and scale parameters are derived. However, in practice, the shape parameter is typically unknown. We propose the MLE by a new methodological approach for all three parameters of the heavy-tailed GPD when the shape parameter is unknown. Confidence intervals for the location and scale parameters are constructed by the equal probability density principle. If the shape parameter is known, we can find known distributions of the pivots of the location and scale parameters, but not approximate. While if the shape parameter is unknown, the distributions of the pivots are closed linked to an estimation of the shape parameter. The advantage of our method is that the proposed interval estimation provides the smallest confidence interval, regardless of whether the distribution of the pivot is symmetric. Extensive simulations are used to demonstrate the performance of the point estimation and confidence intervals estimation and show that our method outperforms the traditional technique in most cases.

摘要

我们研究了基于上限记录值的重尾广义帕累托分布 (GPD) 的点估计和置信区间估计。当形状参数已知时，可以导出位置和尺度参数的偏差校正矩估计量和最大似然估计量 (MLE)。然而，在实践中，形状参数通常是未知的。当形状参数未知时，我们通过一种新的方法论方法为重尾 GPD 的所有三个参数提出 MLE。位置和尺度参数的置信区间由等概率密度原则构建。如果形状参数已知，我们可以找到位置和尺度参数的已知分布，但不是近似的。而如果形状参数未知，枢轴的分布与形状参数的估计密切相关。我们方法的优点是，无论主元的分布是否对称，所提出的区间估计都提供了最小的置信区间。广泛的模拟用于证明点估计和置信区间估计的性能，并表明我们的方法在大多数情况下优于传统技术。