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Matrix variate Birnbaum-Saunders distribution under elliptical models. (English) Zbl 1441.62136
Summary: This paper derives the elliptical matrix variate version of the well known univariate Birnbaum-Saunders distribution [Z. W. Birnbaum and S. C. Saunders, J. Appl. Probab. 6, 319–327 (1969; Zbl 0209.49801)]. A generalisation based on a matrix transformation is proposed, instead of the independent element-to-element elliptical extension of the Gaussian univariate case. Some results on Jacobians were needed to derive the new matrix variate distribution. A number of particular distributions are studied and some basic properties are found. Finally, an example based on real data of two populations is given and the maximum likelihood estimates are obtained for the class of Kotz models. A comparison with the Gaussian kernel is also given by using a modified BIC criterion.
##### MSC:
 62H10 Multivariate distribution of statistics 62N05 Reliability and life testing 62E15 Exact distribution theory in statistics 60E05 Probability distributions: general theory 15A23 Factorization of matrices 15A09 Theory of matrix inversion and generalized inverses 15B52 Random matrices (algebraic aspects)
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