对数正态分布参数估计的积分变换矩法应用

Integral transform method of moment in estimating parameters of lognormal distribution and its application

针对对数正态分布参数估计矩法存在的缺陷,探讨了梅林变换的应用,推导了参数对应的一般矩和对数矩,提出了一种对数正态分布参数估计方法-积分变换矩法,包括二参数对数正态分布和三参数对数正态分布。以西南诸河16个水文站为例,利用三参数对数正态分布作为水文频率线型,对年平均流量系列进行了拟合。结果表明,与矩法相比,积分变换矩法能明显提高Cs的估算精度。

Aiming at the defects of method of moments（MOM） for estimating the parameters of lognormal distribution,the application of Mellin transform theory is discussed,and the general moment and logarithmic moment are derived respectively;the integral transform method of moment（ITMOM） for parameter estimation is put forward,including two-parameter lognormal distribution and three-parameter lognormal distribution.By taking 16 hydrological stations in Yunnan province as example,the annual averages discharge are fitted by using three-parameter lognormal distribution as the hydrologic frequency curves.The result shows that compared with the MOM,the calculation precision of C_s obviously increased by the new method.