A simple but powerful modification of the standard Gaussian distribution is studied. The variables of the rectified Gaussian are constrained to be nonnegative, enabling the use of nonconvex energy functions. Two multimodal examples, the competitive and cooperative distributions, illustrate the representational power of the rectified Gaussian. Since the cooperative distribution can represent the...

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...

an estimation problem of the mean µ of an inverse gaussian distribution ig(µ, c µ) with known coefficient of variation c is treated as a decision problem with entropy loss function. a class of bayes estimators is constructed, and shown to include mrse estimator as its closure. two important members of this class can easily be computed using continued fractions