Preservation of the log concavity by Bernstein operator with an application to ageing properties of a coherent system

Abstract

In this paper, we provide a new proof of the preservation of the log concavity by Bernstein operator. It is based on the bivariate characterization of the likelihood ratio order. In addition, we give new conditions under which the previous property leads to preservation of ageing properties in coherent systems with independent and identically distributed components.