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...

Health care interventions which use quality of life or health scores often provide data which are skewed and bounded. The scores are typically formed by adding up responses to a number of questions. Different questions might have different weights, but the scores will be bounded, and are often scaled to the range 0 to 100. If improvement in health over time is measured, scores will tend to clus...

In this paper we define and study a three-parameter distribution, referred to as the Beta skew-normal distribution (BSN), which is a generalization of the skewnormal distribution introduced by Azzalini [1]. This family is obtained using the generator approach suggested by Eugene et al. [2] and Jones [3]. Some properties of the proposed distribution are discussed: among others the moment generat...

In this paper we discuss a Bayesian analysis of the scalar skew-normal model. This model defines a class of distributions that extends the Gaussian model by including a shape parameter. Although the skew-normal model has nice properties, it presents some problems with the estimation of the shape parameter. To avoid these drawbacks, we explore through some examples the use of Severini’s integrat...

A class of multivariate extended skew-t (E ST ) distributions is introduced and studied in detail, along with closely related families such as the subclass of extended skew-normal distributions. Besides mathematical tractability and modeling flexibility in terms of both skewness and heavier tails than the normal distribution, the most relevant properties of the E ST distribution include closure...

Shannon and Rényi entropies are two important measures of uncertainty for data analysis. These have been studied multivariate Student-t skew-normal distributions. In this paper, we extend the entropy to skew-t finite mixture (FMST) This class flexible distributions allows handling asymmetry tail weight behavior simultaneously. We find upper lower bounds these families. Numerical simulations ill...

In this article, we introduce the multivariate slash and skew-slash t distributions which provide alternative choices in simulating and fitting skewed and heavy tailed data. We study their relationships with other distributions and give the densities, stochastic representations, moments, marginal distributions, distributions of linear combinations and characteristic functions of the random vect...

In this paper, we assume the error distribution of one-way ANOVA as alpha-skew normal distribution. Alpha-skew gives us exibility for modelling data which has heavy tailness, skewness, bimodality and also symmetricity. We obtain maximum likelihood estimator model parameters test statistics based on these estimators. Monte Carlo simulation study states that estimators interest are more efficient...