Abstract:
This study focuses on the development of a generalised multivariate beta type II distribution
as well as the noncentral and bimatrix counterparts with positive domain. These
models emanate from a sequential quality monitoring procedure with the normal and
multivariate normal distributions as the underlying process distributions. Three different
scenarios are considered, namely:
1. The variance is monitored from a normal process and the mean remains unchanged;
2. The above-mentioned scenario but the known mean also encounters a sustained
shift;
3. The covariance structure of a multivariate normal distribution is monitored with
the known mean vector unchanged.
The statistics originating from the above-mentioned scenarios considered are constructed
from different dependent chi-squared or Wishart ratios. Exact expressions are derived for
the probability density functions of these statistics. These new distributions contribute
to the statistical discipline in the sense that it can serve as alternatives to existing probability
models, and can be used in determining the performance of the quality monitoring
procedure.
