Linear functions of order statistics from bivariate, exchangeable, continuous and elliptical random vectors have a skew-elliptical distribution. This result generalizes previous ones on order statistics and skewed distributions.

The sum of squares and products matrix has a Wishart distribution, when the rows of the corresponding data matrix are i.i.d. according to a skew-normal distribution centered at the origin. Applications include robustness of the t-test, time series and spatial statistics.

This paper provides a unified treatment and a Bayesian interpretation of two different classes of multivariate skew-normal distributions proposed by Azzalini and Dalla Valle (Biometrika 83 (1996) 715) and Gupta et al. (Tech. Rep., Cimat, Mexico (2001)). We show that the above classes of...

This paper shows that linear functions of order statistics (L-statistics) based on exchangeble random samples have a Fundamental Skew distribution (Arellano-Valle and Genton, 2003). The paper also examines the exact distribution of L.statistics when the sampled population is Skew-Normal. Exact...

Multivariate random sums appear in many scientific fields, most notably in actuarial science, where they model both the number of claims and their sizes. Unfortunately, they pose severe inferential problems. For example, their density function is analytically intractable, in the general case,...

Fisher’s linear discriminant function might be difficult to estimate, when data come from a semiparametric, finite mixture model. We propose an estimator based on the singular value decomposition of the third standardized cumulant. The estimator is consistent when sampling from a mixture of...