Box-Cox Transformation

Box-Cox Transformation

Box-Cox Transformation

Description

The Box-Cox transformation is a mathematical technique that transforms a non-normal or skewed dataset into a more normal distribution.

Why to use

  • Normality
  • Homoscedasticity
  • Linearity

When to use

  • Non-Normal data


When not to use

  • Negative or zero values

Prerequisites

  • Continuous variable
  • Positive values
  • Handling Outliers
  • Choice of lambda

Input

Any dataset containing numerical variables.

Output

A transformed dataset that follows a more normal distribution.

Statistical Methods Used

  • Maximum Likelihood Estimation (MLE)
  • Method of moments

Limitations

  • Limited applicability
  • Sensitivity to outliers
  • Subjectivity in lambda selection
  • Interpretability
  • Data assumptions

The Box-Cox transformation is a statistical technique that transforms non-normal or skewed data into a more normal distribution. It involves applying a power transformation to the data using a lambda parameter. The specific formula for the change is:

where,

 is the transformed variable,

     is the original variable, and

    is the transformation parameter.


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