Mixture of Experts (MoE) is a popular framework in the fields of statistics and machine learning for modeling heterogeneity in data for regression, classification and clustering. MoE for continuous data are usually based on the normal distribution. However, it is known that for data with asymmetric behavior, heavy tails and atypical observations, the use of the normal distribution is unsuitable...

By further generalizing the concept of Hermitian (or normal) and skew-Hermitian splitting for a non-Hermitian and positive-definite matrix, we introduce a new splitting, called positive-definite and skew-Hermitian (PS) splitting, and then establish a class of positivedefinite and skew-Hermitian splitting (PSS) methods similar to the Hermitian (or normal) and skew-Hermitian splitting (HSS or NSS...

Main academic criticism on the Sharpe ratio concerns its lack in incorporating skewness in performance evaluation. In this note we rewrite the classical Sharpe ratio for skew normal distributions. This new skew-normal Shape ratio consistently moves with skewness and no distorted information on performance is provided. An empirical investigation illustrates skew-normality of mutual and hedge fun...

Fertility rate is one of the most important global indexes. Past researchers found models which fit to age-specific fertility rates. For example, mixture probability density functions have been proposed for situations with bi-modal fertility patterns. This model is less useful for unimodal age-specific fertility rate patterns, so a model based on skew-symmetric (skew-normal) pdf was proposed by...

We establish an identity for $$Ef\left( \varvec{Y}\right) - Ef\left( \varvec{X}\right) $$ , when $$\varvec{X}$$ and $$\varvec{Y}$$ both have matrix variate skew-normal distributions the function f satisfies some weak conditions. The characteristic of skew normal distribution is then derived. make use it to derive necessary sufficient conditions comparison under six different orders, such as usu...

We develop a Bayesian approach for the selection of skew in multivariate skew t distributions constructed through hidden conditioning in the manners suggested by either Azzalini and Capitanio (2003) or Sahu, Dey and Branco (2003). We show that the skew coefficients for each margin are the same for the standardized versions of both distributions. We introduce binary indicators to denote whether ...

hail phenomenon is one of the hazardous weather phenomena that can make the highest amount of damage to farms, gardens, cars, rooftops, etc. in a very short time (a few minutes), depending on the diameter of the particles. one of the best ways to study this devastating climatic phenomenon is the use of atmospheric instability indices. the indices which are calculated with the help of radiosonde...

many researchers have been efforted to identify the shape of distribution of stress and strength of castellated beam and base on that, offer a method for design that members. through this methods, comparing virendil method by simplicity and reasonable results, have been used widly. regardless from shortcoming of this method, there is two idea for distribution of stresses via primary bending in ...

This paper is concerned with the multivariate extended skew-normal [MESN] and skew-Student [MEST] distributions, that is, distributions in which location parameters of underlying truncated are not zero. The extra parameter leads to greater variability moments critical values, thus providing flexibility for empirical work. It reported this various theoretical properties notably limiting forms as...