Transforms

Box-Cox Transformations

greybox.transforms.bc_transform(y: ndarray, lambda_bc: float) → ndarray[source]: Box-Cox transformation.

greybox.transforms.bc_transform_inv(y: ndarray, lambda_bc: float) → ndarray[source]: Inverse Box-Cox transformation.

Box-Cox Transformation

The Box-Cox transformation is defined as:

\[\begin{split}y^{(\lambda)} = \begin{cases} \frac{y^\lambda - 1}{\lambda} & \text{if } \lambda \neq 0 \\ \ln(y) & \text{if } \lambda = 0 \end{cases}\end{split}\]

Common Values

lambda=0 : Log transformation
lambda=0.5 : Square root transformation
lambda=1 : No transformation (linear)
lambda=-1 : Inverse transformation

Example

from greybox import bc_transform, bc_transform_inv

# Apply Box-Cox transformation with lambda=0.5
y_transformed = bc_transform([1, 4, 9, 16], lambda_bc=0.5)
# Result: [0, 2, 4, 6]

# Inverse transformation
y_original = bc_transform_inv([0, 2, 4, 6], lambda_bc=0.5)
# Result: [1, 4, 9, 16]

mean_fast

greybox.transforms.mean_fast(x: ndarray, df: int | None = None, trim: float = 0.0, side: str = 'lower') → float[source]: Fast mean calculation with optional trimming.

The mean_fast function computes a trimmed/hubered mean that is robust to outliers.

Parameters

x : array-like - Input data
df : int - Degrees of freedom (default: 1)
trim : float - Trim proportion (0 to 0.5, default: 0.0)
side : str - Trim side: “both” (default), “lower”, or “upper”

Example

from greybox import mean_fast
import numpy as np

data = np.array([1, 2, 3, 4, 5, 100])

# Standard mean (affected by outlier)
np.mean(data)  # ~19.17

# Trimmed mean (remove 10% from each tail)
mean_fast(data, trim=0.1)  # ~3.0