Abstract
Let X 1, …, X n be a sequence of independent real random variables with common distribution function F and density function f. Let be the corresponding order statistics and let denote the associated spacings. Define the empirical distribution function of the spacings. It is known that G n,F converges. We characterize completely the distributions F which give the same G F as well as the set of GF's when f describes the set of all densities on. Moreover, given a limiting function G, we construct all the distributions F for which G F = G. In addition we establish two Tauberian theorems which relate the behaviour of G F at infinity (resp. in 0) to the behaviour of f at infinity (resp. in 0 when f has a singularity at the origin).
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