Box-Cox transformation — g

Evaluate the Box-Cox transformation, which is a scaled power transformation to preserve continuity in the index lambda at zero. Negative values are permitted.

Usage

g_bc(t, lambda)

Arguments

t: argument(s) at which to evaluate the function
lambda: Box-Cox parameter

Value

The evaluation(s) of the Box-Cox function at the given input(s) t.

Note

Special cases include the identity transformation (lambda = 1), the square-root transformation (lambda = 1/2), and the log transformation (lambda = 0).

Examples

# Log-transformation:
g_bc(1:5, lambda = 0); log(1:5)
#> [1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379
#> [1] 0.0000000 0.6931472 1.0986123 1.3862944 1.6094379

# Square-root transformation: note the shift and scaling
g_bc(1:5, lambda = 1/2); sqrt(1:5)
#> [1] 0.0000000 0.8284271 1.4641016 2.0000000 2.4721360
#> [1] 1.000000 1.414214 1.732051 2.000000 2.236068