simdata_uniform: Generates random variates from multivariate uniform...
In sortinghat: sortinghat

Description Usage Arguments Details Value Examples

We generate n observations from each of K_0 multivariate uniform distributions such that the Euclidean distance between each of the populations and the origin is equal and scaled by Δ ≥ 0.

1	simdata_uniform(n = rep(25, 5), delta = 0, seed = NULL)

`n`	a vector (of length K_0) of the sample sizes for each population
`delta`	the fixed distance between each population and the origin
`seed`	seed for random number generation. (If `NULL`, does not set seed)

To define the populations, let x = (X_1, …, X_p)' be a multivariate uniformly distributed random vector such that X_j \sim U(a_j^{(k)}, b_j^{(k)}) is an independently distributed uniform random variable with a_j^{(k)} < b_j^{(k)} for j = 1, …, p.

For each population, we set the mean of the distribution along one feature to Δ, while the remaining features have mean 0. The objective is to have unit hypercubes with p = K_0 where the population centroids separate from each other in orthogonal directions as Δ increases, with no overlap for Δ ≥ 1.

Hence, let (a_k^{k}, b_k^{(k)}) = c(Δ - 1/2, Δ + 1/2). For the remaining ordered pairs, let (a_j^{(k)}, b_j^{(k)}) = (-1/2, 1/2).

We generate n_k observations from kth population.

For Δ = 0, the K_0 = 5 populations are equal.

Notice that the support of each population is a unit hypercube with p = K_0 features. Moreover, for Δ ≥ 1, the populations are mutually exclusive and entirely separated.

named list containing:

x:: A matrix whose rows are the observations generated and whose columns are the p features (variables)
y:: A vector denoting the population from which the observation in each row was generated.

data_generated <- simdata_uniform(seed = 42)
dim(data_generated$x)
table(data_generated$y)

data_generated2 <- simdata_uniform(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))