Distributional equations of the form are studied, where x and y are neighboring generalized order statistics based on distribution function f, and v is a power function or pareto distributed random variable, independent of y. Characterizations of distributions via random contraction and random dilation are stated involving three conditions, namely, the distributional equation, the form of f and the distribution of v, where each two assertions imply the third. Recent results for the particular submodels of order statistics and record values are contained and also extended.
Beutner, E. A., & Kamps, U. (2008). Randon contraction and random dilation of generalized order statistics. Communications in Statistics - Theory and Methods, 37(14), 2185-2201. https://doi.org/10.1080/03610920701877594