Description
Return logit=ln(value/(1-value)) and margin=min(value-epsilon,1-epsilon-value).
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 logit=ln(value/(1-value)) and margin=min(value-epsilon,1-epsilon-value).
When to use this tool
Use Bounded Logit Scalar Domain Margin 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, epsilon. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read logit, margin. Use the output convention below.
Require 0<epsilon<0.5 and epsilon<=value<=1-epsilon. Return logit=ln(value/(1-value)) and margin=min(value-epsilon,1-epsilon-value).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Supplied scalar or returned value under the stated operation. | Required. Finite number. |
| epsilon | Epsilon | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| logit | Logit | Required. Finite number. |
| margin | Nonnegative distance to the supplied epsilon bounds, not to zero/one directly. | Required. Finite number. |
{
"input": {
"value": 0.5,
"epsilon": 0.25
},
"output": {
"logit": 0,
"margin": 0.25
}
}Limitations and assumptions
- The tool rejects values outside the supplied bounded interval rather than clamping them. Margin is a distance to that interval's edges; extremely tiny epsilon can round 1-epsilon to one and still produce a nonfinite-result error at the upper endpoint.
- 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
Similar or alternative tools
- Unit Interval Epsilon Clamp Distance
Return clamped and distance=abs(value-clamped).
- Log Scaler Positive Domain Distance
Return distance=value-lowerBoundary and valid=(value>lowerBoundary).