Wishart ratios with dependent structure: New members of the bimatrix beta type IV |
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Authors: | A Bekker JJJ Roux |
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Institution: | a Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, South Africa b Faculty of Mathematics, Shahrood University of Technology, Shahrood, Iran |
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Abstract: | In multivariate statistics under normality, the problems of interest are random covariance matrices (known as Wishart matrices) and “ratios” of Wishart matrices that arise in multivariate analysis of variance (MANOVA) (see 24). The bimatrix variate beta type IV distribution (also known in the literature as bimatrix variate generalised beta; matrix variate generalization of a bivariate beta type I) arises from “ratios” of Wishart matrices. In this paper, we add a further independent Wishart random variate to the “denominator” of one of the ratios; this results in deriving the exact expression for the density function of the bimatrix variate extended beta type IV distribution. The latter leads to the proposal of the bimatrix variate extended F distribution. Some interesting characteristics of these newly introduced bimatrix distributions are explored. Lastly, we focus on the bivariate extended beta type IV distribution (that is an extension of bivariate Jones’ beta) with emphasis on P(X1<X2) where X1 is the random stress variate and X2 is the random strength variate. |
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Keywords: | Primary: 62H10 Secondary: 62E15 |
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