Sarkar (1998) showed that certain positively dependent (MTP2) random variables satisfy the Simes inequality. The multivariate-t distribution does not satisfy this (MTP2) property, so other means are necessary. A corollary was given in Sarkar (1998) to handle this distribution, but there is an...

The normal density is unimodal in a strong sense as are the densities of mixtures of normals whose means are not too far apart. Consequently, by a standard result in reliability, these mixture densities have an increasing failure rate. This paper investigates how the modality of mixtures of...