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...

In recent years, the skew-normal models introduced in Azzalini (1985) have enjoyed an amazing success, although an important literature has reported that they exhibit, in the vicinity of symmetry, singular Fisher information matrices and stationary points in the profile log-likelihood function for skewness, with the usual unpleasant consequences for inference. For general multivariate skew-symm...

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...

Normal state-space models are prevalent, but to increase the applicability of the Kalman filter, we propose mixtures of skewed, and extended skewed, Kalman filters. To do so, the closed skew-normal distribution is extended to a scalemixture class of closed skew-normal distributions. Some basic properties are derived and a class of closed skew-t distributions is obtained. Our suggested family of...

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...