Huang Mei Ling, Raney-Yan Xiang
Department of Mathematics, Brock University, St. Catharines, ON L2S 3A1, Canada.
Department of Mathematcs, Niagara College, Welland, ON L3C 7L3, Canada.
Entropy (Basel). 2021 Jan 4;23(1):70. doi: 10.3390/e23010070.
The high quantile estimation of heavy tailed distributions has many important applications. There are theoretical difficulties in studying heavy tailed distributions since they often have infinite moments. There are also bias issues with the existing methods of confidence intervals (CIs) of high quantiles. This paper proposes a new estimator for high quantiles based on the geometric mean. The new estimator has good asymptotic properties as well as it provides a computational algorithm for estimating confidence intervals of high quantiles. The new estimator avoids difficulties, improves efficiency and reduces bias. Comparisons of efficiencies and biases of the new estimator relative to existing estimators are studied. The theoretical are confirmed through Monte Carlo simulations. Finally, the applications on two real-world examples are provided.
重尾分布的高分位数估计有许多重要应用。研究重尾分布存在理论困难，因为它们往往具有无穷矩。高分位数的现有置信区间（CI）方法也存在偏差问题。本文提出了一种基于几何均值的高分位数新估计器。新估计器具有良好的渐近性质，并且提供了一种用于估计高分位数置信区间的计算算法。新估计器避免了困难，提高了效率并减少了偏差。研究了新估计器相对于现有估计器的效率和偏差比较。通过蒙特卡罗模拟证实了理论结果。最后，给出了两个实际例子的应用。
