Description
Differentiate population weighted variance with respect to one observation weight, accounting for the moving weighted mean.
A statistical term depends on its data summaries, weighting convention, centering, denominator, and boundary rules. A contribution, derivative, domain check, or converted summary answers a narrower question than a complete estimator. Those conventions must match before terms are combined or compared.
Differentiate population weighted variance with respect to one observation weight, accounting for the moving weighted mean.
When to use this tool
Use Weighted Variance One Weight Derivative when you need this specific summary conversion, contribution, domain rule, or sensitivity term with matching statistical conventions.
How to use the tool and how it works
- Enter value, mean, variance, totalWeight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read derivative. Use the output convention below.
Return derivative=((value-mean)²-variance)/totalWeight with nonnegative variance and positive totalWeight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| mean | Mean | Required. Finite number. |
| variance | Variance | Required. Finite number; minimum 0. |
| totalWeight | Total Weight | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| derivative | Derivative | Required. Finite number. |
{
"input": {
"value": 7,
"mean": 3,
"variance": 4,
"totalWeight": 10
},
"output": {
"derivative": 1.2
}
}Limitations and assumptions
- This is the derivative of a normalized weighted second central moment with respect to one weight while observations are fixed. Supplied summaries are not recomputed or verified; it is not an unbiased sample-variance derivative.
- The field tables state structural bounds; the mechanics also specify cross-field constraints. Malformed inputs and unsupported domains cause errors. A successful false flag, empty branch value, or zero placeholder has the meaning stated above and is distinct from an input error.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Use a complete estimator or model when a contribution, sensitivity, or domain check is insufficient. Verify the weight semantics, centering, denominator, and sampling assumptions before combining summaries.
References
Similar or alternative tools
- Weighted Mean Missing Weight Budget
Combine observedWeight*observedMean with missingWeight times each supplied missing bound, dividing by the positive combined weight for lowerMean and upperMean.
- Weighted Mean One Weight Sensitivity
Return derivative=(value-mean)/totalWeight for positive totalWeight.