The Box-Cox transformation is a flexible transformation, often used to transform data towards normality. The modulus transformation generalises Box-Cox to also work with negative values.
1 2 3
Transformation exponent, λ.
Constant offset. 0 for Box-Cox type 1,
otherwise any non-negative constant (Box-Cox type 2).
The Box-Cox power transformation (type 1) requires strictly positive values and
takes the following form for
y > 0:
y^(λ) = (y^λ - 1)/λ
y = 0, the natural log transform is used.
The modulus transformation implements a generalisation of the Box-Cox
transformation that works for data with both positive and negative values.
The equation takes the following forms, when
y != 0 :
y^(λ) = sign(y)*((|y|+1)^λ - 1)/λ
y = 0:
y^(λ) = sign(y) * ln(|y| + 1)
Box, G. E., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society. Series B (Methodological), 211-252. https://www.jstor.org/stable/2984418
John, J. A., & Draper, N. R. (1980). An alternative family of transformations. Applied Statistics, 190-197. http://www.jstor.org/stable/2986305
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