对数正态分布参数的精确估计及其应用

分析了两参数对数正态分布均值四种常见的估计方法,其中Gunnar Taraldsen提出的修正极大似然估计优于其他三种估计。在此基础上讨论了总体m阶原点矩和m阶中心矩以及峰度的修正极大似然估计,而且提出总体的中位数、众位数和偏度不存在修正的极大似然估计,并用Mathematica 4.0对上海股票市场的大盘日成交量进行仿真分析,结果表明与理论推导完全一致。

Precise estimation and application of log-normal distribution parameters

The four estimators of mean of two parameters log-normal distributin were analyzed,in which the modified MLE given by Gunnar Taraldsen was the excellent estimator.On the basis of this,the modified MLE of the m-exponent original matrix,the m-exponent central matrix and kurtosis were discussed.Moreover,it is proposed that the median,mode and skewness do not exist the modified MLE.And Shanghai Stock Exchange is artificially analyzed by Mathematica 4.0,the result shows that it is completely consistent with theoretical derivation.