Convergence rate to a lower tail dependence coefficient of a skew-t distribution

We examine the rate of decay to the limit of the tail dependence coefficient of a bivariate skew t distribution which always displays asymptotic tail dependence. It contains as a special case the usual bivariate symmetric t distribution, and hence is an appropriate (skew) extension. The rate is asymptotically power-law. The second-order structure of the univariate quantile function for such a skew-t distribution is a central issue.Comment: 14 page

The Kumaraswamy Skew-t Distribution and Its Related Properties

Skew normal distribution has been introduced by Azzalini (1985) as an alternative to the normal distribution to accommodate asymmetry. Since then extensive studies have been done on applying Azzalini’s skewness mechanism to other well-known distributions, such as skew-t distribution which is more flexible and can better accommodate long tailed data than the skew normal one. Cordeiro and de Castro (2011) proposed a new class of distribution called the Kumaraswamy generalized distribution (Kw − F) which is capable of fitting skewed data that cannot be fitted well by existing distributions. Since then, the Kw −F distribution has been widely studied and various versions of generalization of this distribution family have been introduced. In this paper we introduce a new generalization of the skew-t distribution based on the Kumaraswamy generalized distribution. The new class of distribution which we call the Kumaraswamy skew-t (KwST) has the ability of fitting skewed, long and heavy tailed data and is more flexible than the skew-t distribution as it contains the skew-t distribution as a special case. Related properties of this distribution family such as mathematical properties, moments, and order statistics are discussed. The proposed distribution is applied to a real data set to illustrate the estimation procedure

Accounting and governance risk forecasting in the health care industry

Previous authors have proved the advantage of commercial Accounting and Governance Risk (AGR) evaluation methods over academic methods. However, the information used in commercial methods is not readily available to an investor. Therefore, the most important features used in academic methods and the AGR was forecast by Random Forests. It found a weak relation between the AGR rating and share price data (Close and Volume), using a skew t-distribution. For visualisation we used the Kohonen map, which identified three clusters. Clusters revealed AGR increasing, decreasing trendsetting and cluster-based companies which appear to have no clear trend. A self-organised map (SOM) used the AGR history of alpha-stable distribution parameters, which were calculated from the stock data (Close and Volume). Also, the test sample (companies rating data), following from skew t-distribution, has been simulated by maximum likelihood method, and parameters of the skew t-distribution have been estimated

Distributions generated by perturbation of symmetry with emphasis on a multivariate skew tt distribution

A fairly general procedure is studied to perturbate a multivariate density satisfying a weak form of multivariate symmetry, and to generate a whole set of non-symmetric densities. The approach is general enough to encompass a number of recent proposals in the literature, variously related to the skew normal distribution. The special case of skew elliptical densities is examined in detail, establishing connections with existing similar work. The final part of the paper specializes further to a form of multivariate skew $t$ density. Likelihood inference for this distribution is examined, and it is illustrated with numerical examples.Comment: full-length version of the published paper, 31 pages with 9 figure

Bayesian Nonlinear Regression Models based on Slash Skew-t Distribution

This paper considers the Bayesian analysis for estimating the parameters of nonlinear regression model when the error term has a slash skew-t distribution. This model is an asymmetric nonlinear regression model which is suitable for fitting the data sets with heavy tail and skewness. The properties of this model are derived and a hierarchical representation of this model based on the stochastic representation of slash skew-t distribution is given. This representation allows us to use Markov Chain Monte Carlo method to estimate the parameters of model. To compare this model with other asymmetric nonlinear regression models, we use conditional predictive ordinate statistic and deviance information, expected Akaike information and expected Bayesian information criterions, and show the performance of the proposed model by a simulation study. Also an application of the new model to fitting a real data set is discussed