Boxcox Input Unit Exponent Factor Tool

Description

Unit rescaling identity for the unnormalized Box-Cox transform, with the logarithmic lambda-zero limit.

Normalization depends on the supplied center, scale, norm, range, reference distribution, or denominator. A zero spread and a missing denominator need an explicit policy, and clipping differs from fitting a scaler. Evaluating one scalar or derivative term does not estimate every parameter or establish a distributional improvement.

Unit rescaling identity for the unnormalized Box-Cox transform, with the logarithmic lambda-zero limit.

When to use this tool

Use Boxcox Input Unit Exponent Factor when you already have the required normalization parameters and need this local scalar, range, policy, or derivative term.

How to use the tool and how it works

Enter scaleFactor, lambda, transformed. Use the units and conventions below.
Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
Read multiplicativeFactor, additiveShift, scaledTransform. Use the output convention below.

For positive scaleFactor return multiplicativeFactor=scaleFactor^lambda and additiveShift=ln(scaleFactor) when lambda==0, otherwise expm1(lambda*ln(scaleFactor))/lambda. Return scaledTransform=multiplicativeFactor*transformed+additiveShift.^[1]

Input field	Meaning and units	Accepted input
scaleFactor	Scale Factor	Required. Finite number; strictly above 0.
lambda	Lambda	Required. Finite number.
transformed	Transformed	Required. Finite number.

Output field	Interpretation	Returned shape
multiplicativeFactor	Multiplicative Factor	Required. Finite number.
additiveShift	Additive Shift	Required. Finite number.
scaledTransform	Scaled Transform	Required. Finite number.

json

{
  "input": {
    "scaleFactor": 2,
    "lambda": 1,
    "transformed": 3
  },
  "output": {
    "multiplicativeFactor": 2,
    "additiveShift": 1,
    "scaledTransform": 7
  }
}

Limitations and assumptions

This assumes transformed is already a compatible Box-Cox value for the same lambda. It adjusts for multiplying the original positive input by scaleFactor, without validating an underlying input, fitting lambda, or standardizing the output.
Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.

Alternative or Complementary methods

Fit or verify the intended scaler parameters and statistical model separately. Check units, zero policies, missingness, clipping, inverse conventions, and whether supplied norms or denominators belong to the same data.

References

Calculation and input contract: normalize/boxcox-input-unit-exponent-factor — tool.io

Similar or alternative tools

Boxcox Lambda Zero Continuity Bridge
For positive value return zeroLimit=ln(value) and transformed=zeroLimit when lambda==0, otherwise expm1(lambda*ln(value))/lambda.
Affine Normalizer Parameter Compose
For first transform y=firstScale*x+firstOffset followed by z=secondScale*y+secondOffset return scale=secondScale*firstScale and offset=secondScale*firstOffset+secondOffset.