The multivariate Behrens–Fisher distribution

The Multivariate Gaussian Distribution

A vector-valued random variable X = X 1 · · · X n T is said to have a multivariate normal (or Gaussian) distribution with mean µ ∈ R n and covariance matrix Σ ∈ S n ++ 1 if its probability density function 2 is given by p(x; µ, Σ) = 1 (2π) n/2 |Σ| 1/2 exp − 1 2 (x − µ) T Σ −1 (x − µ). We write this as X ∼ N (µ, Σ). In these notes, we describe multivariate Gaussians and some of their basic prope...

The Complex Multivariate Gaussian Distribution

Here I introduce package cmvnorm, a complex generalization of the mvtnorm package. A complex generalization of the Gaussian process is suggested and numerical results presented using the package. An application in the context of approximating the Weierstrass σ-function using a complex Gaussian process is given.

The multivariate skew-slash distribution

The slash distribution is often used as a challenging distribution for a statistical procedure. In this article, we define a skewed version of the slash distribution in the multivariate setting and derive several of its properties. The multivariate skew-slash distribution is shown to be easy to simulate from and can therefore be used in simulation studies. We provide various examples for illust...

Screening for a Multivariate Mixture Normal Distribution

Multivariate Bernoulli Distribution

In this paper, we consider the multivariate Bernoulli distribution as a model to estimate the structure of graphs with binary nodes. This distribution is discussed in the framework of the exponential family, and its statistical properties regarding independence of the nodes are demonstrated. Importantly the model can estimate not only the main effects and pairwise interactions among the nodes b...