三参数Weibull分布的秩拟合最优化法

对于给定的一组疲劳寿命试验数据，首先求得该样本顺序统计量的平均秩（或中位秩），然后由三参数Ｗｅｉｂｕｌ分布对此平均秩进行拟合．通过对线性拟合相关系数的最优化求解来确定Ｗｅｉｂｕｌ分布的位置参数，再由最小二乘拟合便可估计出Ｗｅｉｂｕｌ分布的形状参数和尺度参数．该方法具有迭代收敛快且拟合精度高的特点．

Optimization Method of Mean Rank Fitting of Three Parameter Weibull Distribution

A method of fitting the three parameter Weibull distribution to the mean or median rank of the order statistic of a given sample of fatigue life is presented. An optimization procedure is established to obtain location parameter of Weibull distribution, which corresponds to the maximum of the absolute value of the linear regression coefficient. Both the shape parameter and the characteristic parameter are estimated by using the method of least square regression. It is showed that this new method of parameter estimation of Weibull distribution is very accurate as well as very fast in convergence.