Biweight Scale

This function computes the biweight scale, a robust measure of scale or dispersion for a numeric vector. The biweight scale is less sensitive to outliers than the sample standard deviation.

Usage

biweight_scale(
  x,
  loc = stats::median(x),
  c = 9,
  reduced = FALSE,
  tol = 1e-06,
  max_iter = 50,
  drop.na = FALSE
)

Arguments

x

A numeric vector.

loc

Initial guess for the location (default: median of x).

c

A numeric value specifying the tuning constant for the biweight estimator (c = 9 by default).

reduced

A logical value specifying whether the sample size, n, should be reduced to the number of non-rejected values. If TRUE, n is reduced to the number of observations that pass a rejection criteria. If FALSE (default), n is equal to the length of x (the input data).

tol

Convergence tolerance for the iterative computation (default: 1e-6).

max_iter

Maximum number of iterations (default: 50).

drop.na

A logical value indicating whether to remove missing values (NA) from the calculations. If TRUE, missing values will be removed. If FALSE (the default), missing values will be included in the calculations.

Value

The biweight scale of x.

References

• Mosteller, F., and Tukey, J. W. (1977). Data Analysis and Regression: A Second Course in Statistics. Addison-Wesley, pp. 203-209.

Author

Christian L. Goueguel

Examples

# Example 1: Compute biweight scale for a vector
x <- c(seq(1,100))
tibble::tibble(
sd = stats::sd(x),
mad = stats::mad(x),
biscale = biweight_scale(x)
)
#> # A tibble: 1 × 3
#>      sd   mad biscale
#>   <dbl> <dbl>   <dbl>
#> 1  29.0  37.1    29.6

# Example 2: Biweight scale is robust to outliers
x <- c(seq(1,99), 1e3) # An outlier at 1000
tibble::tibble(
sd = stats::sd(x),
mad = stats::mad(x),
biscale = biweight_scale(x)
)
#> # A tibble: 1 × 3
#>      sd   mad biscale
#>   <dbl> <dbl>   <dbl>
#> 1  99.2  37.1    29.5