Flexible Class of Skew‐Symmetric Distributions

Abstract

We propose a flexible class of skew-symmetric distributions for which the probability density function has the form of a product of a symmetric density and a skewing function. By constructing an enumerable dense subset of skewing functions on a compact set, we are able to consider a family of distributions, which can capture skewness, heavy tails and multimodality systematically. We present three illustrative examples for the fibreglass data, the simulated data from a mixture of two normal distributions and the Swiss bills data. Copyright 2004 Board of the Foundation of the Scandinavian Journal of Statistics..

A Model for Age-Specific Fertility Rate Pattern of India Using Skew-Logistic Distribution Function

“…The skew-normal density is the key representative of skew-symmetric family. For more insight into the properties of this family, the readers may refer to Genton [22] and a review paper of Azzalini [24].…”

“…The above model in (7) is unimodal curve [22]. Mazzuca and Scarpa [23] used the generalized skew-normal, which is termed as Flexible Generalized Skew-Normal (FGSN) distribution to fit bimodal fertility schedule.…”

Likelihood Inference of Nonlinear Models Based on a Class of Flexible Skewed Distributions

“…The actual situation is that it is not rare at all to encounter multimodality, sometimes with an even more irregular shape, and, for this case, the aforementioned distributions become unsufficient. In this paper, with the adoption of a sufficiently flexible class of distributions, we consider one of these extensions, referred to as the family of flexible skew-symmetric (FSS) distributions which is introduced by [9] with the following density function of type:…”

“…Following this idea, the skw-normal (SN) distribution was firstly introduced by [4], and, then, the skew-t (ST) distribution was introduced by [5]; the skew-t-normal (STN) was introduced by [6]; moreover, some extensions to these multivariate cases were studied by [7,8] and so on. Since then, several authors have tried to extend these results to more general forms of skew-symmetric distributions, of which here we would like to mention [9], in this paper; they proposed a general framework of distributions which is called flexible skewsymmetric (FSS) distribution. As pointed out by [10] that this distribution family enjoys a sufficient flexibility in that with different choice of submodel settings, the FSS distribution includes several known distributions such as the SN and ST as its special cases.…”

Multivariate extremes of generalized skew-normal distributions

“…1 for an example. This class of distributions, introduced by Ma and Genton (2004), can systematically model light tails, multimodality and skewness. If we take K = 1, H = Φ (the stan- The density and contours of a bivariate flexible skew-normal distribution with ξ = 0, Ω = I 2 , H = Φ, K = 3, and P K (x, y) = x + y − 4x 2 y − 2xy 2 + 2x 3 − y 3 .…”