Description
Return transformed=-L when a==0, otherwise -expm1(a*L)/a, plus logarithmicBranch on that exact equality.
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.
Return transformed=-L when a==0, otherwise -expm1(a*L)/a, plus logarithmicBranch on that exact equality.
When to use this tool
Use Yeojohnson Negative Branch Boundary 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 value, lambda. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read transformed, logarithmicBranch. Inspect logarithmicBranch before interpreting the associated values.
For value<=0 set a=2-lambda and L=log1p(-value). Return transformed=-L when a==0, otherwise -expm1(a*L)/a, plus logarithmicBranch on that exact equality.1
The negative-input Yeo-Johnson formula uses exponent 2-lambda, with a logarithmic branch at lambda two. This tool evaluates that branch, including its zero boundary, without estimating lambda.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Supplied scalar or returned value under the stated operation. | Required. Finite number; maximum 0. |
| lambda | Finite supplied Yeo-Johnson parameter; lambda two uses the logarithmic branch. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| transformed | Transformed | Required. Finite number. |
| logarithmicBranch | Logarithmic Branch | Required. Boolean. |
{
"input": {
"value": -3,
"lambda": 2
},
"output": {
"transformed": -1.3862943611198906,
"logarithmicBranch": true
}
}Limitations and assumptions
- This implements only the nonpositive Yeo-Johnson branch, with the logarithmic limit at lambda two. It does not fit lambda, standardize data, evaluate positive inputs, or guarantee finite results for extreme parameters.
- 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/yeojohnson-negative-branch-boundary — tool.io
-
SciPy Reference: Yeo-Johnson Transform — SciPy Community
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.
- Boxcox Input Unit Exponent Factor
Unit rescaling identity for the unnormalized Box-Cox transform, with the logarithmic lambda-zero limit.