Log-concavity and monotonicity of hazard and reversed hazard functions of univariate and multivariate skew-normal distributions

Abstract

This paper establishes the log-concavity property of several forms of univariate and multivariate skew-normal distributions. This property is then used to prove the monotonicity of the hazard as well as reversed hazard functions. The log-concavity and monotonicity of the hazard and reversed hazard functions of series and parallel systems of components is then discussed. The corresponding results for the multivariate normal distribution follow readily as special cases.