= L. S. Nelson
{c}
<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.<The Folded Normal Distribution by F. C. Leone and others>[Publisher abstract, estimation problem and tabulated assistance]{ref}
The distinction between the observed mean and the signed mean is important. For $Y=|X|$ with $X\sim N(\mu,\sigma^2)$, $Y^2=X^2$, so
$$
\mathbb E Y^2=\mu^2+\sigma^2.
$$
A 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.
The verified source prints the author as L. S. Nelson. A shared surname and initials are insufficient to attach a separate biography or portrait without a source linking the records.
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