The known estimation and simulation methods for multivariate t distributions are reviewed. A review of selected applications is also provided. We believe that this review will serve as an important reference and encourage further research activities in the area.

The noncentral t–distribution is intimately tied to statistical inference procedures for samples from normal populations. For simple random samples from a normal population the usage of the noncentral t–distribution includes basic power calculations, variables acceptance sampling plans (MIL– STD–414) and confidence bounds for percentiles, tail probabilities, statistical process control paramete...

The traditional estimation of mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers or heavy-tailed errors. A robust mixture regression model based on the t−distribution by extending the mixture of t−distributions to the regression setting is proposed. However, this proposed new mixture regression model is still not robust to high leve...

A central assumption in generative grammar research on the relationship between syntax and the lexicon is that syntax is a projection of the lexicon. The structure of sentences is a refl ection of the lexical properties of the individual lexical items they contain. In the standard view, each lexical item is associated with a lexical entry that contains three kinds of information, as indicated i...

Beta-t-EGARCH models in which the dynamics of the logarithm of scale are driven by the conditional score are known to exhibit attractive theoretical properties for the t-distribution and general error distribution (GED). The generalized-t includes both as special cases. We derive the information matrix for the generalized-t and show that, when parameterized with the inverse of the tail index, i...

The empirical distribution of daily returns from financial market variables such as exchange rates, equity prices, and interest rates, is often skewed, having one heavy, and one semiheavy, or more Gaussian-like tail. The NIG distribution, that has two semi-heavy tails, models skewness rather well, but only in cases where the tails are not too heavy. On the other hand, the skew Student’s t-distr...

Normal mixture models are being increasingly used to model the distributions of a wide variety of random phenomena and to cluster sets of continuous multivariate data. However, for a set of data containing a group or groups of observations with longer than normal tails or atypical observations, the use of normal components may unduly affect the fit of the mixture model. In this paper, we consid...

This paper introduces measures of information for Bayesian analysis when the support of data distribution is truncated progressively. The focus is on the lifetime distributions where the support is truncated at the current age t>=0. Notions of uncertainty and information are presented and operationalized by Shannon entropy, Kullback-Leibler information, and mutual information. Dynamic updatings...