Value-at-Risk (VaR) is a widely used statistical measure in financial risk management for quantifying the level of risk associated with a specific investment portfolio. It is well-known that historical return data exhibit non-normal features, such as heavy tails and skewness. Current analytical (parameteric) calculation of VaR typically assumes the distribution of the portfolio return to be a n...

This paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. Firit, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a sing...

This paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. First, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a sing...

We report a skew-Laplace statistical analysis of both flow cytometry scatters and cell size from microbial strains primarily grown in batch cultures, others in chemostat cultures and bacterial aquatic populations. Cytometry scatters best fit the skew-Laplace distribution while cell size as assessed by an electronic particle analyzer exhibited a moderate fitting. Unlike the cultures, the aquatic...

In this paper, the skew-elliptical sinh-alpha-power distribution is developed as a natural follow-up to log-linear Birnbaum–Saunders alpha-power distribution, previously studied in literature. Special cases include ordinary and skewed distributions. As shown, it able surpass sinh-normal models when fitting data sets with high (above expected sinh-normal) degrees of asymmetry. Maximum likelihood...

In many practical situations, we only know a few first moments of a random variable, and out of all probability distributions which are consistent with this information, we need to select one. When we know the first two moments, we can use the Maximum Entropy approach and get normal distribution. However, when we know the first three moments, the Maximum Entropy approach doe snot work. In such ...

Abstract In this article, a large class of univriate Birnbaum–Saunders distributions based on the scale shape mixture skew normal is introduced which generates suitable subclasses for modeling asymmetric data in variety settings. The moments and maximum likelihood estimation procedures are disscused via an ECM-algorithm. observed information matrix to approximate asymptotic covariance parameter...

In this article, we deal European style option, with arbitrary payoff which includes both put and call options, on an asset whose price evolves as It?-McKean skew Brownian motion Azzalini skew-normal distribution. Initially, investigate a condition leads the to be martingale. Next, option show that if function is convex then so function. After this, finite satisfies partial differential equatio...