Log-concavity of generalized order statistics

Generalized order statistics have been introduced as a unification of several models of random variables arranged in ascending order of magnitude with different interpretations and statistical applications. The purpose of this note is to investigate conditions on the underlying distribution function and on the parameters under which the generalized order statistics and their spacings have log-concave joint densities, respectively. Several well-known results in the literature are complemented and strengthened.

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