In this paper, the S&P 500 stock index is studied for its time varying volatility and stylized facts. The ARMA mean equation with asymmetric power ARCH errors is used to model the series correlations and the conditional heteroscadesticity in the asset returns. The conditional distributions of the standardized residuals are assumed to be the normal distribution, the t distribution or the skew-t ...

In this paper, likelihood-based inference and bias correction based on Firth’s approach are developed in the modified skew-t-normal (MStN) distribution. The latter model exhibits a greater flexibility than skew-normal (MSN) distribution since it is able to heavily skewed data thick tails. addition, tails controlled by shape parameter degrees of freedom. We provide density new present some its m...

In this paper we study the multivariate skew-normal distribution and its scale mixtures, as extensions of the similar non-skewed distributions. Different parameterizations and some properties are investigated. ∗ Subject Classification: 60E05.

In this paper, multivariate skew-normal distribution is em- ployed for analyzing an outcome based dropout model for repeated mea- surements with non-random dropout in skew regression data sets. A probit regression is considered as the conditional probability of an ob- servation to be missing given outcomes. A simulation study of using the proposed methodology and comparing it with a semi-parame...

Approximating a binomial distribution by a suitable normal distribution is a well known practice, and widely discussed in introductory level statistics books. Recently it has been shown (in Chang et al. (2008)) that the skew-normal distributions can provide a far better approximation than the normal ones. This article revisits the approximation issue and other related inferential aspects. Thoug...

The Skew Normal (SN, hereafter) class of densities has posed several and interesting inferential problems. In particular, the maximum likelihood estimator of the shape parameter λ may take infinite values with positive sampling probability. To overcome these problems we propose an objective Bayesian approach, based on reference priors. We show that the reference prior for λ is proper when λ is ...

The evaluation of future cash flows and solvency capital recently gained importance in general insurance. To assist in this process, our paper proposes a novel loss reserving model, designed for individual claims in discrete time. We model the occurrence of claims, as well as their reporting delay, the time to the first payment, and the cash flows in the development process. Our approach uses d...

The entropy and mutual information index are important concepts developed by Shannon in the context of information theory. They have been widely studied in the case of the multivariate normal distribution. We first extend these tools to the full symmetric class of multivariate elliptical distributions and then to the more flexible families of multivariate skew-elliptical distributions. We study...