Clustering Via Nonparametric Density Estimation: the R Package pdfCluster

The R package pdfCluster performs cluster analysis based on a nonparametric estimate of the density of the observed variables. After summarizing the main aspects of the methodology, we describe the features and the usage of the package, and finally illustrate its working with the aid of two datasets

Statistical applications of the multivariate skew-normal distribution

Azzalini & Dalla Valle (1996) have recently discussed the multivariate skew-normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.Comment: full-length version of the published paper, 32 pages, with 7 figures, uses psfra

The information matrix of the bivariate extended skew-normal distribution

For the extended skew-normal distribution, which represents an extension of the normal (or Gaussian) distribution, we focus on the properties of the log-likelihood function and derived quantities in the the bivariate case. Specifically, we derive explicit expressions for the score function and the information matrix, in the observed and the expected form; these do not appear to have been examined before in the literature. Corresponding computing code in R language is provided, which implements the formal expressions

Some properties of the unified skew-normal distribution

For the family of multivariate probability distributions variously denoted as unified skew-normal, closed skew-normal and other names, a number of properties are already known, but many others are not, even some basic ones. The present contribution aims at filling some of the missing gaps. Specifically, the moments up to the fourth order are obtained, and from here the expressions of the Mardia's measures of multivariate skewness and kurtosis. Other results concern the property of log-concavity of the distribution, and closure with respect to conditioning on intervals