Multivariate log-skewed distributions with normal kernel and their applications

Abstract

We introduce two classes of multivariate log skewed distributions with normal kernel: the log canonical fundamental skew-normal (log-CFUSN) and the log unified skew-normal (log-SUN).We also discuss some properties of the log-CFUSN family of distributions. These new classes of log-skewed distributions include the log-normal and multivariate log-skew normal families as particular cases. We discuss some issues related to Bayesian inference in the log-CFUSN family of distributions, mainly we focus on how to model the prior uncertainty about the skewing parameter. Based on the stochastic representation of the log-CFUSN family, we propose a data augmentation strategy for sampling from the posterior distributions. This proposed family is used to analyze the US national monthly precipitation data. We conclude that a high dimensional skewing function lead to a better model fit.

Shannon entropy and Kullback–Leibler divergence in multivariate log fundamental skew‐normal and related distributions

“…However, multivariate versions of such univariate distributions are usually intractable. In [22] the authors introduced the LCFUSN family of distributions in the following way. Let Z = (Z 1 , .…”

“…However multivariate versions of such univariate distributions are usually intractable. Queiroz, Loschi, & Silva () introduced the LCFUSN family of distributions in the following way. Let be an random vector and consider the transformations and .…”

“…Suppose we want to quantify the amount of information brings about when has distribution in the CFUSN or the LCFUSN family. As these families are closed under marginalization (Queiroz, Loschi, & Silva, ; Arellano‐Valle & Genton, ), from Equation we obtain in the following cases: if , and ; if , and …”

“…In Proposition 3 we obtain the entropy of the LCFUSN distribution introduced by Queiroz, Loschi, & Silva () whose pdf is given in Equation .…”

“…In recent years, the interest in new parametric distributions able to model skewness, heavy tails, bimodality and some other data characteristics that are not well fitted by the usual distributions is growing. Seeking for flexible and tractable distributions to model non-negative data and motivated by some results that recently appeared in [23], the multivariate logcanonical fundamental skew-normal (LCFUSN) family of distributions is introduced in [22]. 1 marinamunizdequeiroz@gmail.com 2 rogerwcs@ufmg.br 3 loschi@ufmg.br Our purpose in this work is to explore some properties of the LCFUSN family that are useful to solve relevant problems, such as the quantification of the information in a system or the definition of optimal designs.…”