Let $\Pi_m$ denote the $m$th population with a
$p$-dimensional multivariate Student's t
distribution, $T_p(\mu_m, \Sigma_m, c_m)$, where
$\mu_m$ is the population location vector,
$\Sigma_m$ is the positive-definite covariance
matrix, and $c_m$ is the degrees of freedom. Let $e_m$ be the $m$th standard basis vector
(i.e., the $m$th element is 1 and the remaining
values are 0). Then, we define $$\mu_m = \Delta
\sum_{j=1}^{p/M} e_{(p/M)(m-1) + j}.$$ Note that p
must be divisible by M. By default, the first 10
dimensions of $\mu_1$ are set to delta with
all remaining dimensions set to 0, the second 10
dimensions of $\mu_2$ are set to delta with
all remaining dimensions set to 0, and so on.
We use a common covariance matrix $\Sigma_m = \Sigma$
for all populations.
For small values of $c_m$, the tails are heavier,
and, therefore, the average number of outlying
observations is increased.
By default, we let $M = 5$, $\Delta = 0$,
$\Sigma_m = I_p$, and $c_m = 6$, $m = 1,
\ldots, M$, where $I_p$ denotes the $p \times p$
identity matrix. Furthermore, we generate 25 observations
from each population by default.
For $\Delta = 0$ and $c_m = c$, $m = 1,
\ldots, M$, the $M$ populations are equal.