Weibull分布参数估计方法及其应用

PARAMETER ESTIMATE METHOD APPLICATION OF WEIBULL DISTRIBUTION

Ｗｅｉｂｕｌｌ分布对于年最大风速、波高、降水量等气候极值具有很高的拟合精度和很强的适应性。本文给出四种Ｗｅｉｂｕｌｌ分布参数估计方法：概率权重矩法（ＰＷＭ）、最小二乘法（ＬＳＭ）、最大似然法（Ｍ－Ｌ）和适线法（ＦＩＴ），并通过统计检验进行拟会精度比较。结果表明：ＰＷＭ、ＬＳＭ和Ｍ－Ｌ法对样本的拟合精度都比较高，其中ＰＷＭ法计算最为简便，ＬＳＭ和Ｍ－Ｌ法采取ａ０的试设法，大大简化了计算过程；经验累积频率公式更适合于Ｗｅｉｂｕｌｌ分布；三参数计算精度较二参数高得多。

Weibull distribution is of great fitting precision and good adaptability for maxmum wind speed. height of wave and precipitation. Four parameter estimate methods of Weibull distribution are given in this paper. They are probability weighted momented (PWM) .least square method (LSM) . maxmum likelihood (M-L) and fitting (FIT) respectively. The results of statistical tests show that fitting precision of PWM . LSM and M-L methods is higher than others, and PWM method is the most convenient. The calculating processes in LSM and M-L methods are greatly simplified because of the assumption of parameter a0. The formula of experience accumulation frequency Pi= is better fit to Weibull distribution than others. The calculation precision using three parameters is much higher than that of using two parameters.