P-Ⅲ分布参数估计方法的研究

Study of Parameter Estimation Methods of Pearson Type- Ⅲ Distribution

本文以参数、设计值及概率不偏性和有效性为评价标准,着重对现行3种主要的P-Ⅲ型分布参数估计方法:概率权重矩法(PWM),绝对值准则适线法及本文提出的可以考虑历史洪水的权函数法,进行了统计试验综合比较研究.比较时对历史洪水的抽样不仅考虑了我国目前广泛使用的个数模型,而且还使用了门限模型.大量计算结果表明:PWM法及绝对值准则适线法是P-Ⅲ型分布参数估计较优良的方法.

Based upon the Monte-Carlo experiments, the main parameter estimation methods of P- Ⅲ distribution are discussed and comprehensively compared in the paper, including methods of moments, maximum likelihood, curve fitting, probability weighted moments (PWM) and several weighted function moments which have been developed recently in China. In the comparision, flood series with extraordinary flood are generated not only in chinese given-number model, but also in Stedinger-Hirsch model (threshold model). The criteria for evaluation an estimation method are considered from two aspects. One is the unbiasness and efficiency of the parameter and design flood value with given probability, the other is the unbiasness and efficiency of the probability of failure of design flood. Many culculations show that PWM and curve fitting method with absolute norm are the two best estimation methods of P- Ⅲ distribution.