Draw random numbers from unusual distributions, such as on the unit or non-negative real line with known means and standard deviations.
rmultiunit(
n,
mean,
sd,
Sigma = NULL,
Omega = NULL,
perfect_correlation = FALSE
)
rmultiunit_from_real(
n,
mean_real,
sd_real = NULL,
Sigma_chol = NULL,
perfect_correlation = FALSE
)
runit_from_real(n, mean_real, sd_real)
runit(n, mean, sd)
unit_to_real(unit_mean, unit_sd)number of random draws to simulate. Each draw is a vector of
values with length equal to length(mean) and
length(sd) and the resulting output has n rows
and length(mean) columns
vector of mean values on the unit scale
vector of positive standard deviations
optional covariance matrix with dimensions of
length(mean) by length(mean) defining covariances
between each pair of values in mean. Note that only
the correlation structure is retained from Sigma,
so that standard deviations are still required
optional correlation matrix with dimensions of
length(mean) by length(mean) defining correlations
between each pair of values in mean
logical, if TRUE
and Sigma and Omega are NULL, then all
values in each replicate (row) are perfectly correlated with known
mean and standard deviation. If FALSE, then all values
in each replicate are completely uncorrelated
vector of mean values converted to real-line equivalents
vector of standard deviations converted to real-line equivalents
Cholesky decomposition of covariance matrix converted to real-line equivalent
vector of mean values on the unit interval
vector of standard deviations on the unit interval
The r*unit family of functions support simulation of values
on the unit interval based on a known mean, sd, and correlation
structure. runit and runit_from_real are vectorised
univariate functions, and rmultiunit and
rmultiunit_from_real are multivariate versions of these
same functions. runit and rmultiunit provide
simulated values on the unit line with specified means, standard
deviations, and correlation/covariance structure (in the case of
rmultiunit).
The *_from_real versions of these functions are helpers
that use pre-transformed estimates of parameters on the real
line, calculated with unit_to_real. These functions
are exported because unit_to_real, called within
runit and rmultiunit, is slow. Separating
this into a separate step allows less frequent calculations
of this transformation using function or dynamic versions
of args in simulate.
unit_to_real converts means and standard deviations
from their values on the unit line to their equivalent
values on the real line.
The use of the different versions of these functions is illustrated in the Macquarie perch example on the package [website](https://aae-stats.github.io/aae.pop/).
# rmultiunit generates multivariate draws constrained to
# the unit interval, with known mean, standard deviation,
# and (optionally) covariance/correlation structure
rmultiunit(n = 10, mean = c(0.25, 0.5, 0.75), sd = c(0.1, 0.4, 0.25))
#> [,1] [,2] [,3]
#> [1,] 0.3913312 0.8967120724 0.5251920
#> [2,] 0.2627124 0.0210964696 0.6988087
#> [3,] 0.2946292 0.9810610591 0.9535728
#> [4,] 0.3279317 0.7477435199 0.4582237
#> [5,] 0.2337661 0.0002655617 0.9493458
#> [6,] 0.2134636 0.9157487816 0.6829384
#> [7,] 0.1900636 0.9940835701 0.4050700
#> [8,] 0.1778885 0.9775295742 0.8532240
#> [9,] 0.2431005 0.5722960618 0.7541516
#> [10,] 0.2760783 0.9671427349 0.7984281
if (FALSE) {
# add in a correlation structure
omega_set <- cbind(
c(1, 0.25, 0.01),
c(0.25, 1, 0.5),
c(0.01, 0.5, 1)
)
rmultiunit(
n = 10,
mean = c(0.25, 0.5, 0.75),
sd = c(0.1, 0.4, 0.25),
Omega = omega_set
)
}