The Elfving distribution is defined as 
The distribution is named after Finnish statistician and mathematician Gustav Elfving (1908-1984), who described the distribution in 1947 .
In his Biometrika paper, Elfving established a distributional result concerning order statistics. Specifically, he investigates the distribution of the sample range when the samples are drawn from a standard normal distribution. Previous work on exact calculations for finite samples were found to be intractable . Elfving tackled the problem from a different direction, determining the asymptotic distribution of the sample range for large samples.
Elfving Distribution Alternatives
Elfving’s distribution has a distinct disadvantage over other methods, which may be why it’s little discussed outside of a few historical references. While other methods can be expressed directly in terms of the range, Elfving’s formula involves a non-linear transformation of the range, making it a theoretical challenge . For example, Gumbel’s method  leads to the same results as Elfving’s distribution; however, Gumbel’s method requires no knowledge of sample size, the analytical form of the initial distribution, or numerical values of the distribution’s parameters.
 Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.
 Elfing, G. (1947). The asymptotical distribution of range in samples from a normal population. Biometrika 34 111–119.
 Nordstrom, K. (1999). The Life and Work of Gustav Elfving. Statistical Science. Vol. 14, No. 2, 174-196.
 Cox, D. R. (1948). A Note on the Asymptotic Distribution of Range. Biometrika, 35(3/4), 310–315. https://doi.org/10.2307/2332353
 Gumbel, E. (1949). Probability tables for the range. Biometrika, 36: 142-148.