L. S. Nelson

L. S. Nelson is a coauthor, with F. C. Leone and R. B. Nottingham, of the 1961 paper The Folded Normal Distribution by F. C. Leone and others. It develops estimation of the underlying normal distribution's mean and standard deviation from measurements reported as absolute values, with tables and an example to support the procedure.^[ref]

The distinction between the observed mean and the signed mean is important. For $Y=|X|$ with $X\sim N(\mu ,{\sigma }^2)$, $Y^2=X^2$, soA second moment alone does not separate offset from spread. For example, $(\mu ,\sigma )=(0,1)$ and $(0.6,0.8)$ both give $\mathbb{E}{Y}^2=1$, although their full folded normal distributions differ. Additional distributional information or moments are needed to distinguish these cases.

When $\mu =0$, the observed mean is $\sigma \sqrt{2/\pi }$, about $0.798\sigma$, rather than zero. Interpreting the average absolute deviation as the original signed mean would therefore create an apparent positive offset even for a centered normal distribution. These elementary consequences explain the measurement problem addressed by the joint paper; they are illustrative derivations rather than an attribution of a particular calculation to Nelson alone.

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