The multivariate Behrens–Fisher distribution (original) (raw)
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A Bayesian solution to the Behrens–Fisher problem
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2021
A simple solution to the Behrens-Fisher problem based on Bayes factors is presented, and its relation with the Behrens-Fisher distribution is explored. The construction of the Bayes factor is based on a simple hierarchical model, and has a closed form based on the densities of general Behrens-Fisher distributions. Simple asymptotic approximations of the Bayes factor, which are functions of the Kullback-Leibler divergence between normal distributions, are given, and it is also proved to be consistent. Some examples and comparisons are also presented.
On Some Characteristics of the Bivariate T-Distribution
The bivariate t-distribution is a natural generalization of the bivariate normal distribution as a derived sampling distribution. For broad spectrum of researchers, the paper emphasizes the bivariate t-distribution as a mixture of bivariate normal distribution and an inverted chi-square distribution. Moments and related characteristics of the distribution are presented from this perspective.
Default Bayesian analysis of the Behrens–Fisher problem
Journal of Statistical Planning and Inference, 1999
In the Bayesian approach, the Behrens-Fisher problem has been posed as one of estimation for the di erence of two means. No Bayesian solution to the Behrens-Fisher testing problem has yet been given due, perhaps, to the fact that the conventional priors used are improper. While default Bayesian analysis can be carried out for estimation purposes, it poses di culties for testing problems. This paper generates sensible intrinsic and fractional prior distributions for the Behrens-Fisher testing problem from the improper priors commonly used for estimation. It allows us to compute the Bayes factor to compare the null and the alternative hypotheses. This default procedure of model selection is compared with a frequentist test and the Bayesian information criterion. We ÿnd discrepancy in the sense that frequentist and Bayesian information criterion reject the null hypothesis for data, that the Bayes factor for intrinsic or fractional priors do not.
On the Multivariate T-Distribution and Some of its Applications
This paper makes an attempt to justify a multivariate t -model and provides a modest review of most important results of this model developed in recent years. Essential properties and applications of the model in various fields are discussed. Special attention is given to pre-test and shrinkage estimation for regression parameters under certain restrictions. The predictive distributions under the multivariate t -distribution are also discussed. It is observed that the multivariate t -distribition is more convincing to model multivariate data than multivariate normal distribution because of its fat tail.
Generalized multivariate Birnbaum–Saunders distributions and related inferential issues
Journal of Multivariate Analysis, 2013
Birnbaum and Saunders introduced in 1969 a two-parameter lifetime distribution which has been used quite successfully to model a wide variety of univariate positively skewed data. Diaz-Garcia and Leiva-Sanchez [9] proposed a generalized Birnbaum-Saunders distribution by using an elliptically symmetric distribution in place of the normal distribution. Recently, Kundu et al.
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A Note on the Characteristic Function of Multivariate t Distribution
Communications for Statistical Applications and Methods, 2014
This study derives the characteristic functions of (multivariate/generalized) t distributions without contour integration. We extended Hursts method (1995) to (multivariate/generalized) t distributions based on the principle of randomization and mixtures. The derivation methods are relatively straightforward and are appropriate for graduate level statistics theory courses.