求韦泊分布三参数的一种方法

本文介绍了求韦泊分布三参数ａ，ｂ和ｃ的最小二乘估计的一种迭代搜索方法。先证明了误差平方和Ｑ（ａ，ｂ，ｃ）是ａ，ｂ和ｃ的连续函数，并具有连续一阶偏导数，和．然后在此基础上引进求ｍｉｎＱ（ａ，ｂ，ｃ）的梯度抛物线顶点搜索法，并与传统的回归方法进行比较。用不同林龄的２１个同龄林胸径总体验算表明，此法可获得精度较高的三参数估计值，而传统的回归方法误差较大，不可取。

A Method of Solving Three Parameters of Weibull Distribution

In this paper a recursive search method for least square estimators of the threeparameters of Weibull distribution is introduced.First ,the sum of squares of errorsQ(a,b,c)as a function of a,b and c,and its first-order derivatives to be continuousare proved.Then a method of finding minQ(a,b,c) by searching for the vertex of a parabolaalong the anti-gradient direction repeatedly is presented.The method is then compared withthe regression method which is often used in this case.Tests with data(breast heightdiameter)from 21 populations of even-aged Jack pine stands show that the method couldyield very high estimates of a,b and c and that results yielded by the regression method arevery poor and unacceptable.