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A study of a transformation preserving independence for beta distributions leads to a new functional equation which is solved under the assumption of local integrability of the functions involved.
Abstract. In the paper we study regressional versions of Lukacs characterization of the gamma law. We consider constancy of regression instead of Lukacs independence condition in three new schemes. Up to now the constancy of regressions of U=X/(X + Y) given V=X + Y for independent X and Y has been considered in the literature. Here we are concerned with constancy of regressions for X and Y while independence...
Abstract. Let X1,X2,,Xn be a random sample from a continuous distribution with the corresponding order statistics X1:nX2:nXn:n. All the distributions for which E(Xk+r: n|Xk:n)=aXk:n+b are identified, which solves the problem stated in Ferguson (1967).
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