正規分布, 対数正規分布およびピアソンIII型分布のPWM解

抄録

It has been considered that a new statistical parameter estimation method using probability weighted moments (PWM) is difficult to be applied for the distributions that cannot be expressed in an inverse form, i. e., x=x(F). The authors show in this paper that it has been successfully applied and that the analytical PWM solutions were obtained for the representative distributions of non-inverse type, that is, Normal, 3-parameter Lognormal and 3-parameter Pearson-III distributions. The PWM estimate of the standard deviation of the Normal distribution turned out to be unbiased and having a form of a linear combination of samples.