ON CHARACTERIZING DISTRIBUTIONS VIA LINEARITY OF REGRESSION FOR ORDER STATISTICS

summary Let X1Xn be a random sample from an absolutely continuous distribution with the corresponding order statistics X1:n≤X2:n≤Xn:n. A complete solution of the problem, posed in 1967 by T. Ferguson, of determining the distribution by linearity of regression of Xk+2:n with respect to Xk:n is given. The only possible distributions are of the exponential, power and Pareto type. A linear regression relation for exponents of order statistics is also considered.

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