In the present article, we derive an explicit expression for truncated mean and variance multivariate normal distribution with arbitrary rectangular double truncation. We use moment generating approach of Tallis (1961) extend it to general ?, ? all combinations As part solution, also give a formula bivariate marginal density multinormal variates. prove invariance property some elements inverse ...

Several formulations have long existed in the literature form of continuous mixtures normal variables where a mixing variable operates on mean or variance both and multivariate variable, by changing nature these basic constituents from constants to random quantities. More recently, other mixture-type constructions been introduced, core component, which operation operates, is not necessarily nor...

We show that lower-dimensional marginal densities of dependent zero-mean normal distributions truncated to the positive orthant exhibit a mass-shifting phenomenon. Despite multivariate density having mode at origin, assigns increasingly small mass near origin as dimension increases. The phenomenon accentuates with stronger correlation between random variables. This surprising behavior has serio...