The

mean vector [[mu].sub.k] is initialized by the median vector, since mean and median are same for normal distribution and the median (Me) is highly robust against outliers with 50% breakdown points to estimate central value of the distribution.

Where [M.sup.i.sub.k] is the median vector of the k-th class from the block training set [B.sup.i] and [M.sup.i] is the total

mean vector of all samples from [B.sup.i].

The values of the components'

mean vector are negligible.

Similarly, BT target data can also be simulated by manual setting of component weights in U, following equation (13) and adding the

mean vector [bar.X].

Also, for the T-variate spherical (elliptical) distribution, the probability density function is P[S.sup.T] with respect to the

mean vector, although when the density function is PST, the distribution is not always spherical (elliptical).

The most useful contribution of PCA to the Pareto dataset is that the entire Pareto dataset can be approximated by the

mean vector of the dataset and a linear combination of a specified number of eigenvectors:

The within-class dispersion matrix expresses the dispersion of each sample around the

mean vector, and the between-class dispersion matrix expresses the distance distribution between two sample sets:

This method first derives the sample

mean vector mM and the covariance matrix R as follows:

where each Gaussian component [[phi].sup.k] is parameterized by the

mean vector [[mu].sup.k] of the same length as z and a (d+1) x (d+1) positive definite covariance matrix [[summation].sup.k].

where each Gaussian component [[phi].sup.k] is parameterized by the

mean vector [[mu].sup.k] of the same length as z and a (d + l)x(d + l) positive definite covariance matrix [[summation].sup.k].

A multivariate process is characterized by a

mean vector [mu] and covariance matrix [summation] which describes the quality characteristics and their interrelations.

The Z value is calculated using the formula Z = [nr.sup.2], where n is the number of observations and r is the

mean vector length regarding data distribution.