We study a generalization of a ratio of spacings introduced by Galton in 1902. The ratio proves to be an important building block in the construction of a large sample test for the hypothesis that a distribution from an extremal domain of attraction belongs to the domain of attraction of the Gumbel law.
Segers, J., & Teugels, J. (2000). Testing the Gumbel hypothesis by Galton’s ratio. Extremes : statistical theory and applications in science, engineering and economics, 3(3), 291-303. https://doi.org/10.1023/A:1011411212045 (Original work published 2000)