The Weibull distribution is characterized via the ratio of two upper record statistics. Also the uniform distribution is characterized via the ratio of two lower record statistics. As an application, an improved confidence interval for the Weibull shape parameter is presented.
"Characterizations of the Weibull and uniform distributions using record values." Braz. J. Probab. Stat. 28 (2) 209 - 222, May 2014. https://doi.org/10.1214/12-BJPS202