Martín Jacinto, Parra María Isabel, Pizarro Mario Martínez, Sanjuán Eva L
Departamento de Matemáticas, Facultad de Ciencias, Universidad de Extremadura, 06006 Badajoz, Spain.
Departamento de Matemáticas, Facultad de Veterinaria, Universidad de Extremadura, 10003 Cáceres, Spain.
Entropy (Basel). 2020 Nov 7;22(11):1267. doi: 10.3390/e22111267.
Usual estimation methods for the parameters of extreme value distributions only employ a small part of the observation values. When block maxima values are considered, many data are discarded, and therefore a lot of information is wasted. We develop a model to seize the whole data available in an extreme value framework. The key is to take advantage of the existing relation between the baseline parameters and the parameters of the block maxima distribution. We propose two methods to perform Bayesian estimation. Baseline distribution method (BDM) consists in computing estimations for the baseline parameters with all the data, and then making a transformation to compute estimations for the block maxima parameters. Improved baseline method (IBDM) is a refinement of the initial idea, with the aim of assigning more importance to the block maxima data than to the baseline values, performed by applying BDM to develop an improved prior distribution. We compare empirically these new methods with the Standard Bayesian analysis with non-informative prior, considering three baseline distributions that lead to a Gumbel extreme distribution, namely Gumbel, Exponential and Normal, by a broad simulation study.
常用的极值分布参数估计方法仅使用了一小部分观测值。当考虑块极大值时，许多数据被丢弃，因此大量信息被浪费。我们开发了一个模型来利用极值框架中可用的全部数据。关键在于利用基线参数与块极大值分布参数之间的现有关系。我们提出了两种进行贝叶斯估计的方法。基线分布方法（BDM）包括使用所有数据计算基线参数的估计值，然后进行变换以计算块极大值参数的估计值。改进基线方法（IBDM）是对初始想法的改进，目的是赋予块极大值数据比基线值更大的权重，通过应用BDM来开发改进的先验分布来实现。我们通过广泛的模拟研究，将这些新方法与具有非信息先验的标准贝叶斯分析进行实证比较，考虑三种导致耿贝尔极值分布的基线分布，即耿贝尔分布、指数分布和正态分布。
