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= F. C. Leone
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<Fred C. Leone> coauthored the 1961 paper <The Folded Normal Distribution by F. C. Leone and others> with <L. S. Nelson> and <R. B. Nottingham>. The original paper lists Leone at the Case Institute of Technology. Its motivating problem was industrial measurement in which a difference or deviation is retained but its algebraic sign is lost or disregarded.<The Folded Normal Distribution by F. C. Leone and others>[First page, byline/affiliation, abstract and introduction]{ref}

The resulting <folded normal distribution> combines two possible signed observations at each positive magnitude. If $X$ has <normal distribution> density $f_X$ and $Y=|X|$, then
$$
f_Y(y)=f_X(y)+f_X(-y),\qquad y>0.
$$
The negative side is reflected onto the positive side. It is not simply deleted. At zero signed mean this gives the <half-normal distribution>; a nonzero offset changes the shape while the observation remains nonnegative.

For a concrete constructed example, suppose a measuring device displays distance from a target rather than signed displacement. A true mean displacement $\mu=2$ and its mirror $\mu=-2$, at the same <standard deviation>, give identical recorded-distance distributions. The joint paper treats the distribution and estimation problem induced by that recording convention. Its tables and example connect the mathematical transformation to analysis of measurements.<The Folded Normal Distribution by F. C. Leone and others>[Abstract, moment-based parameter estimation and example]{ref}

The work illustrates a broader principle of <statistical modelling>: specify what the instrument records before selecting the data distribution. A measurement transformation can alter the observed shape without any change in the underlying physical variability.

\Image[https://www.stat.purdue.edu/images/alumni/distinguished-alumni/Leone.jpg]
{title=Fred C. Leone}
{description=Portrait linked in Purdue University's <1993 Distinguished Alumnus Fred C. Leone by Purdue University> notice.}
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 Fred C. Leone (source code)