摘要
对于三参数Weibull分布y=exp{-[(x-c)/b]~a} (其中y为某一物理量X取值超过x的概率),本文给出了两种由观测序列{x_i}和{y_i}确定参数a,b和c的方法。 这两种方法分别按∑[x_i-b(-lny_i)^(1/a)-c]~2=最小和∑[y_i-exp{-[(x_i-c)/b]~a}]=最小的原则来确定。第一种方法采用优选法和线性回归来计算参数值;第二种方法将函数y在参数的近似值附近展开为三元Tayior级数后用逐步订正法求解。文章还给出了计算青岛不同重现期极值高、低气温的应用实例。
In order to estimate the parameters of the Weibull distribution of the form Y = exp {-[(x-c)/b]'} with Y representing the probability that a physical quantity X assumes a value exceeding x, two approaches are proposed for determining the parameters a,b and c from the observed sequences {xi} and {yi} The first approach is based on the requirement to minimize the sum and employs the oprimum seeking method and the linear regression method. The second approach requires bY}Y to be minimum. The function Y is expressed in the form of Taylor's expansion around the approximate values of the parameters and a succesive correction method is used to calculate the parameters. A practical application to estimating the extreme high and low temperatures corresponding to various return periods at Qingdao is given in the present paper.
出处
《海洋科学》
CAS
CSCD
北大核心
1990年第6期1-8,共8页
Marine Sciences
关键词
海流
水位
WEIBULL分布
参数
估计
Weibull distribution, Return period, Optimum seeking method, Taylor expansion
