Directional Outlyingness for Skewed Distribution

This function computes the directional outlyingness of a numeric vector, as proposed by Rousseeuw et al. (2018), which is a measure of outlyingness of data point that takes the skewness of the underlying distribution into account.

Usage

directOutlyingness(
  x,
  cutoff.quantile = 0.995,
  rmZeroes = FALSE,
  maxRatio = NULL,
  precScale = 1e-10
)

Arguments

x

A numeric vector

cutoff.quantile

A numeric value between 0 and 1 specifying the quantile for outlier detection (default: 0.995).

rmZeroes

A logical value. If TRUE, removes values close to zero (default: FALSE).

maxRatio

A numeric value greater than 2. If provided, constrains the ratio between positive and negative scales (default: NULL).

precScale

A numeric value specifying the precision scale for near-zero comparisons (default: 1e-10).

Value

A tibble with columns:

• data: The original numeric values.

• score: The calculated outlyingness score.

• outlier: A logical vector indicating whether each value is a potential outlier or not.

Details

Directional outlyingness takes the potential skewness of the underlying distribution into account, by the splitting the univariate dataset in two half samples around the median. And then apply one-step M-estimator with Huber \(\rho\)-function for scaling each part.

References

• Rousseeuw, P.J., Raymaekers, J., Hubert, M., (2018). A Measure of Directional Outlyingness With Applications to Image Data and Video. Journal of Computational and Graphical Statistics, 27(2):345–359.

Author

Christian L. Goueguel

Examples

vec <- c(1, 5, 3, 9, 2, 6, 4, 8, 7, 1e3)
directOutlyingness(vec)
#> # A tibble: 10 × 3
#>     data   score outlier
#>    <dbl>   <dbl> <lgl>  
#>  1  1000 237.    TRUE   
#>  2     1   1.51  FALSE  
#>  3     2   1.17  FALSE  
#>  4     3   0.839 FALSE  
#>  5     9   0.835 FALSE  
#>  6     8   0.597 FALSE  
#>  7     4   0.504 FALSE  
#>  8     7   0.358 FALSE  
#>  9     5   0.168 FALSE  
#> 10     6   0.119 FALSE