Preservation of Log Concavity by Bernstein Operator Based on Probabilistic Tools with Applications to the Ageing Properties of a Coherent System

F. G. Badía Blasco, J. H. Cha, H. J. Lee, C. Sanguesa Lafuente

Preservation of log concavity by Bernstein operator is a well-known shape
preserving property. Two novel proofs recently appeared in the literature motivate the current work, providing a new approach based on the bivariate characterization of the likelihood ratio stochastic order. In addition, we come up with applications of the shape preserving property to a coherent system with independent and identically distributed components which are obtained by means of the system’s signature representation.

Keywords: bernstein operator, log-concavity, reliability

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