R. B. Nottingham

R. B. Nottingham coauthored The Folded Normal Distribution by F. C. Leone and others with F. C. Leone and L. S. Nelson, published in Technometrics in 1961. Their paper addressed measurements whose algebraic signs were not recorded. Even if a signed quantity follows a normal distribution, its recorded magnitude follows a different probability distribution.^[ref]

The practical issue is information loss during observation. If $X\sim N(\mu ,{\sigma }^2)$ and the instrument reports $Y=|X|$, then $\mu$ and $-\mu$ produce the same folded normal distribution. Thus magnitudes alone cannot distinguish an offset to one side of a reference from an equally large offset to the other side. This conclusion follows from the observation rule, not from the quality of a numerical fitting method.

An illustrative inspection records distances from a reference line but omits which side each point lies on. A pair of signed readings $-2$ and $+2$ becomes two identical magnitudes $2$. Retaining the original signs would preserve a distinction that no later analysis of those two magnitudes can reconstruct. The paper's contribution is to treat this altered observation distribution explicitly rather than fit an ordinary signed normal distribution to magnitude data.

The cited work is jointly authored; the primary byline does not assign individual responsibility for particular formulas or tables. The printed initials are retained here without attaching unrelated biographical records to this author.