
n
observations from each of four
trivariate distributions such that the Euclidean distance
between each of the populations is a fixed constant,
delta
> 0.sim_unif(n = rep(25, 5), delta = 0, seed = NULL)
We generate $n_m$ observations from population $\Pi_m$.
For $\Delta = 0$ and $\rho_m = \rho$, $m = 1, \ldots, M$, the $M$ populations are equal.
Notice that the support of each population is a unit hypercube with 4 features. Moreover, for $\Delta \ge 1$, the populations are mutually exclusive and entirely separated.
data_generated <- sim_unif(seed = 42)
dim(data_generated$x)
table(data_generated$y)
data_generated2 <- sim_unif(n = 10 * seq_len(5), delta = 1.5)
table(data_generated2$y)
sample_means <- with(data_generated2,
tapply(seq_along(y), y, function(i) {
colMeans(x[i,])
}))
(sample_means <- do.call(rbind, sample_means))
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