| 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{xi}和{yi}确定参数a,b和c的方法。 这两种方法分别按∑[xi-b（-lnyi）1/a-c]2=最小和∑[yi-exp{-[（xi-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。 |
| 关键词: Weibull分布 重现期 优选法 Taylor展开 |
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| PARAMETER ESTIMATION OF THE WEIBULL DISTRIBUTION WITH THREE PARAMETERS |
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| Abstract: |
| In order to estimate the parameters of the Weibull distribution of the form y=exp{-[（x-c）/b]a} 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 ∑[xi-b（-lnyi）1/a-c]2 and employs the oprimum seeking method and the linear regression method. The second approach requires ∑[yi-exp{-[（xi-c）/b]a}]2 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. |
| Key words: Weibull distribution, Return period, Optimum seeking method, Taylow expansion |
