基于新扩展Weibull分布的参数估计及应用

Parameter estimation and application based on the new extended Weibull distribution

Weibull分布是Arccosine-X分布族的一个特例,本文提出一种新的具有两参数的Arccosine-Weibull(AC-W)分布。研究了AC-W分布的基本统计性质,使用频率学派的最大似然估计(MLE)方法讨论了AC-W分布的参数估计,并通过蒙特卡罗模拟分析来评估所获得估计量的效率,最后选取一组真实的洪峰数据集,将AC-W与其他竞争分布进行比较。采用AIC、BIC、CAIC和HQIC等信息准则评估AC-W分布在拟合数据方面相较于竞争分布的优越性,证明了AC-W分布的有效性和灵活性。

The Weibull distribution is a special case of the Arccosine-X distribution family.This paper proposes a new Arccosine-Weibull(AC-W)distribution with two parameters and investigates the basic statistical properties of the AC-W distribution.The maximum likelihood estimation(MLE)method of the frequency school was used to discuss the parameter estimation of the AC-W distribution,and the efficiency of the obtained estimates was evaluated through Monte Carlo simulation analysis.Finally,a set of real flood peak datasets was selected to compare the AC-W distribution with other competing distributions.In order to demonstrate the effectiveness and flexibility of the AC-W distribution,information criteria such as AIC,BIC,CAIC,and HQIC were used to evaluate the superiority of the AC-W distribution over the competing distributions in fitting the data.