Two Probability Plots of the Three-Parameter Lognormal Distribution  

作　　者：蒋仁言 

机构地区：[1]College of Automotive and Mechanical Engineering,Changsha University of Scienceand Technology

出　　处：《Journal of Donghua University(English Edition)》2014年第6期757-759,共3页东华大学学报（英文版）

基　　金：National Natural Science Foundation of China(No.71371035)

摘　　要：The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.

关 键 词：three-parameter lognormal distribution probability plot correlation coefficient model selection parameter estimation 

分 类 号：TB114.3[理学—概率论与数理统计]