runif_outside_range {ICSClust}

Uniform distribution outside a given range

Description

Draw from a multivariate uniform distribution outside a given range. Intuitively speaking, the observations are drawn from a multivariate uniform distribution on a hyperrectangle with a hole in the middle (in the shape of a smaller hyperrectangle). This is useful, e.g., for adding random noise to a data set such that the noise consists of large values that do not overlap the initial data.

Usage

runif_outside_range(n, min = 0, max = 1, mult = 2)

Arguments

n

an integer giving the number of observations to generate.

min

a numeric vector giving the minimum of each variable of the initial data set (outside of which to generate random noise).

max

a numeric vector giving the maximum of each variable of the initial data set (outside of which to generate random noise).

mult

multiplication factor (larger than 1) to expand the hyperrectangle around the initial data (which is given by min and max). For instance, the default value 2 gives a hyperrectangle for which each side is twice as long as the range of the initial data. The data are then drawn from a uniform distribution on the expanded hyperrectangle from which the smaller hyperrectangle around the data is cut out. See the examples for an illustration.

Value

A matrix of generated points.

Author(s)

Andreas Alfons

References

#' Alfons, A., Archimbaud, A., Nordhausen, K., & Ruiz-Gazen, A. (2022). Tandem clustering with invariant coordinate selection. arXiv preprint arXiv:2212.06108.

Examples

## illustrations for argument 'mult'

# draw observations with argument 'mult = 2'
xy2 <- runif_outside_range(1000, min = rep(-1, 2), max = rep(1, 2), 
                           mult = 2)
# each side of the larger hyperrectangle is twice as long as 
# the corresponding side of the smaller rectanglar cut-out
df2 <- data.frame(x = xy2[, 1], y = xy2[, 2])
ggplot(data = df2, mapping = aes(x = x, y = y)) + 
  geom_point()

# draw observations with argument 'mult = 4'
xy4 <- runif_outside_range(1000, min = rep(-1, 2), max = rep(1, 2), 
                           mult = 4)
# each side of the larger hyperrectangle is four times as long 
# as the corresponding side of the smaller rectanglar cut-out
df4 <- data.frame(x = xy4[, 1], y = xy4[, 2])
ggplot(data = df4, mapping = aes(x = x, y = y)) + 
  geom_point()