Noncentral elliptical configuration density

Abstract

AMS subject classifications: 62H99 62E05 15A23 15A52 PACS: 62H10 62E15 15A09 15A52 Keywords: Statistical shape theory Configuration density Elliptically contoured distributions Zonal and invariant polynomials Matrix variate Kotz Pearson Bessel and Jensen-logistic distributions a b s t r a c tThe noncentral configuration density, derived under an elliptical model, generalizes and corrects the Gaussian configuration and some Pearson results. Partition theory is then used to obtain explicit configuration densities associated with matrix variate symmetric Kotz type distributions (including the normal distribution), matrix variate Pearson type VII distributions (including t and Cauchy distributions), the matrix variate symmetric Bessel distribution (including the Laplace distribution) and the matrix variate symmetric Jensenlogistic distribution.

Compound and scale mixture of matricvariate and matrix variate Kotz-type distributions

“…From an applied point of view, the Kotz-type distribution has been implemented in many areas of statistics: in statistical inference, see Naik and Plungpongpun (2007) and Sarr and Gupta (2008); in a Bayesian context, see Fang and Li (1990); in reliability, see Díaz-García and Domínguez-Molina (2006); in shape theory, see Caro-Lopera, Díaz-García, and González-Farías (2009), among many other authors and applications.…”

Distribution of the Largest Eigenvalue of an Elliptical Wishart Matrix and Its Simulation

“…Furthermore, it is developed as a matrix-variate distribution, which is described in Gupta and Nagar (1999). Recently, discussion of the exact distribution theory under the elliptical model is specifically examined, for example, Caro-Lopera et al (2010) and Caro-Lopera et al (2014a, 2016. Caro-Lopera et al (2010) introduced a family of matrix-variate elliptically contoured distributions including a matrix-variate normal distribution, Pearson type VII configuration distribution, Kotz type configuration distribution, Bessel configuration distribution, and Jensen-logistic configuration distribution.…”

“…Recently, discussion of the exact distribution theory under the elliptical model is specifically examined, for example, Caro-Lopera et al (2010) and Caro-Lopera et al (2014a, 2016. Caro-Lopera et al (2010) introduced a family of matrix-variate elliptically contoured distributions including a matrix-variate normal distribution, Pearson type VII configuration distribution, Kotz type configuration distribution, Bessel configuration distribution, and Jensen-logistic configuration distribution. As mentioned by Sutradhar and Ali (1989), the elliptical models are generalization of the multivariate normal distribution, accordingly the models have robust statistical characteristics.…”

Some comments on zonal polynomials and their expected values with respect to elliptical distributions

“…The expected values of zonal polynomials play a fundamental role in the expression of many noncentral distributions based on elliptical distributions, see [1]. A detailed study is given in [15] of the expected values of zonal and invariant polynomials with matrix arguments.…”

“…Unfortunately, many of the conclusions reached are incorrect. Some are errors made in the article itself, see [1], but others are the consequence of erroneous results given in [14].…”