Abstract The multivariate normal and the multivariate t distributions belong to the most widely used multivariate distributions in statistics, quantitative risk management, and insurance. In contrast to the multivariate normal distribution, the parameterization of the multivariate t distribution does not correspond to its moments. This, paired with a non-standard implementation in the R package...

In this paper we study the multivariate skew-normal distribution and its scale mixtures, as extensions of the similar non-skewed distributions. Different parameterizations and some properties are investigated. ∗ Subject Classification: 60E05.

In this talk, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, conditional probability density functions and independence are discussed. The definition of extended noncentral skew chi-square distribution is given. The necessary and sufficient condition...

The need to simulate from a positive multivariate normal distribution arises in several settings, specifically in Bayesian analysis. A variety of algorithms can be used to sample from this distribution, but most of these algorithms involve Gibbs sampling. Since the sample is generated from a Markov chain, the user has to account for the fact that sequential draws in the sample depend on one ano...

The pitch dependency of timbres has not been fully exploited in musical instrument identification. In this paper, we present a method using an F0-dependent multivariate normal distribution of which mean is represented by a function of fundamental frequency (F0). This F0-dependent mean function represents the pitch dependency of each feature, while the F0-normalized covariance represents the non...

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses d...

Multivariate statistical process control deserves particular attention in the recent scenario. Though, Hotelling control chart is quite popular and widely used technique in this field but its performance is deteriorated when the underlying distribution of the quality characteristics is not following multivariate normal distribution. Hence the need of developing a non-parametric multivariate con...

A Taylor series approximation to multivariate integrals taken with respect to a multivariate probability distribution is proposed and applied to the computation of multivariate normal probabilities and conditional expectations. The approximation does not require that the multivariate distribution have a structured covariance matrix and, in its simplest form, can be written as the product of uni...