Data standardization to multivariate Pareto scale
Source:R/transformation_functions.R
data2mpareto.RdTransforms the data matrix empirically to the multivariate Pareto scale.
Arguments
- data
Numeric \(n \times d\) matrix, where
nis the number of observations anddis the dimension.- p
Numeric between 0 and 1. Probability used for the quantile to threshold the data.
- na.rm
Logical. If rows containing NAs should be removed.
Value
Numeric \(m \times d\) matrix, where m is the number
of rows in the original data matrix that are above the threshold.
Details
The columns of the data matrix are first transformed empirically to
standard Pareto distributions. Then, only the observations where at least
one component exceeds the p-quantile of the standard Pareto distribution
are kept. Those observations are finally divided by the p-quantile
of the standard Pareto distribution to standardize them to the multivariate Pareto scale.
If na.rm is FALSE, missing entries are left as such during the transformation of univariate marginals.
In the thresholding step, missing values are considered as -Inf.
See also
Other parameter estimation methods:
emp_chi(),
emp_chi_multdim(),
emp_vario(),
emtp2(),
fmpareto_HR_MLE(),
fmpareto_graph_HR(),
loglik_HR()
Other structure estimation methods:
eglatent(),
eglearn(),
emst(),
fit_graph_to_Theta()
Examples
n <- 20
d <- 4
p <- .8
G <- cbind(
c(0, 1.5, 1.5, 2),
c(1.5, 0, 2, 1.5),
c(1.5, 2, 0, 1.5),
c(2, 1.5, 1.5, 0)
)
set.seed(123)
my_data <- rmstable(n, "HR", d = d, par = G)
data2mpareto(my_data, p)
#> [,1] [,2] [,3] [,4]
#> [1,] 0.2470588 0.4200000 1.4000000 0.7000000
#> [2,] 1.0500000 0.6000000 0.3500000 0.2333333
#> [3,] 0.6000000 0.3230769 1.0500000 0.3000000
#> [4,] 0.7000000 0.5250000 0.8400000 1.4000000
#> [5,] 2.1000000 1.4000000 0.6000000 0.6000000
#> [6,] 0.4666667 0.3000000 0.2210526 2.1000000
#> [7,] 0.3818182 2.1000000 0.3818182 1.0500000
#> [8,] 1.4000000 0.8400000 4.2000000 0.4666667
#> [9,] 4.2000000 1.0500000 2.1000000 4.2000000
#> [10,] 0.3230769 4.2000000 0.2100000 0.2470588