A Note on the Multivariate Normal Hazard

A Note on the Article ’ Inference for multivariate normal mixtures ’

Gaussian mixture models provide a flexible tool for data modeling, clustering and classification. We consider the problem of estimating the parameters of a multivariate Gaussian mixture with K components by maximizing the likelihood function. This approach has a theoretical drawback: the likelihood function is unbounded, and the interesting maxima are local maxima in the interior of the paramet...

Screening for a Multivariate Mixture Normal Distribution

A Characterization of the Multivariate Normal Distribution by Using the Hazard Gradient

A b s t r a c t . We give a general result to characterize a multivariate distribution from a relationship between the left truncated mean function and the hazard gradient function. This result allows us to obtain new characterizations of multivariate distributions. In particular, we show that, for the multivariate normal distribution, the simple relationship, obtained in standardized form by M...

A note on multivariate Gauss-Hermite quadrature

The nodes xi and weights wi are uniquely determined by the choice of the domain D and the weighting kernel ψ(x). In fact, one may go as far as to say that the choice of the domain and the kernel defines a quadrature. In particular, the location of the nodes xi are given by the roots of the polynomial of order m in the sequence of orthonormal polynomials {πj} generated by the metric 〈πj|πk〉 := ∫...

A note on commutative multivariate rational series

Direct arguments are presented showing that for rational series in several com muting variables the rational series problem is non computable and closure under Hadamard product fails