Generalized Bimatrix Variate Beta Distribution: Emanating from a Sequential Process

• Activity Number: 602
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Andriette Bekker*+ and Karien Adamski and Schalk Human and JJJ Roux
• Companies: University of Pretoria and University of Pretoria and University of Pretoria and University of Pretoria
• Keywords: generalised bimatrix variate beta distribution ; hypergeometric function of matrix argument ; Meijer's G-function ; sequential process ; shift in process covariance ; zonal polynomials

Abstract

In this paper, we introduce the generalised bimatrix variate beta type II distribution which originated from ratios of Wishart random variates, emanating from monitoring the process covariance structure of q attributes where samples are independent, having been collected from a multivariate normal distribution with known mean and unknown covariance matrix. The two matrix variates that correspond to the two time periods, immediately after the change in the covariance structure took place, will be the focus of this paper. Some properties of this newly derived bimatrix variate distribution are explored and here the reader should note the derivation of the density functions of the determinants of the correlated components of this bimatrix variate distribution that can be useful in monitoring the process. A measure is proposed to determine the probability that a control chart will signal immediately after a change in the covariance matrix, or after one sample. Some percentage points of statistics will be given as an avenue to address the calculation of run-length probabilities within the matrix environment.