The extreme value distribution was developed for modeling extreme-order statistics or extreme events. In this study, we discuss the distribution of the largest extreme. The main objective of this paper is to determine the best estimators of the unknown parameters of the extreme value distribution. Thus, both classical and Bayesian methods are used. The classical estimation methods under consideration are maximum likelihood estimators, moment’s estimators, least squares estimators, and weighted least squares estimators, percentile estimators, the ordinary least squares estimators, best linear unbiased estimators, L-moments estimators, trimmed L-moments estimators, and Bain and Engelhardt estimators. We also propose new estimators for the unknown parameters. Bayesian estimators of the parameters are derived by using Lindley’s approximation and Markov Chain Monte Carlo methods. The asymptotic confidence intervals are considered by using maximum likelihood estimators. The Bayesian credible intervals are also obtained by using Gibbs sampling. The performances of these estimation methods are compared with respect to their biases and mean square errors through a simulation study. The maximum daily flood discharge (annual) data sets of the Meriç River and Feather River are analyzed at the end of the study for a better understanding of the methods presented in this paper.

极值分布是为建模极端顺序统计或极端事件而开发的。在本研究中，我们讨论了最大极值的分布。本文的主要目的是确定极值分布的未知参数的最佳估计量。因此，使用了经典方法和贝叶斯方法。正在考虑的经典估计方法是最大似然估计器、矩估计器、最小二乘估计器和加权最小二乘估计器、百分位估计器、普通最小二乘估计器、最佳线性无偏估计器、L 矩估计器、修剪 L 矩估计器和贝恩和恩格尔哈特估计。我们还为未知参数提出了新的估计器。. 通过使用最大似然估计量来考虑渐近置信区间。贝叶斯可信区间也是通过使用吉布斯采样获得的。通过模拟研究比较了这些估计方法的偏差和均方误差。为了更好地理解本文提出的方法，我们在研究结束时分析了梅里奇河和费瑟河的最大日洪水流量（年度）数据集。