Description
Return contribution=weight*(value-mean)³, requiring nonnegative weight.
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.
Return contribution=weight*(value-mean)³, requiring nonnegative weight.
When to use this tool
Use Third Central Moment Single Deviation 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, weight. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read contribution. Use the output convention below.
Return contribution=weight*(value-mean)³, requiring nonnegative weight.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| value | Value | Required. Finite number. |
| mean | Mean | Required. Finite number. |
| weight | Supplied weight; interpretation follows the stated model rather than an inferred probability. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| contribution | One term under the stated formula, not necessarily a complete statistic. | Required. Finite number. |
{
"input": {
"value": 5,
"mean": 3,
"weight": 0.5
},
"output": {
"contribution": 4
}
}Limitations and assumptions
- This is one unnormalized third-central-moment contribution in cubed measurement units times weight. It does not estimate a mean, divide by total weight, or calculate corrected sample skewness.
- 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
- Central Moment Standardization Term
Standardize a supplied central moment by its declared order; no bias correction or moment estimation.
- Standard Deviation Rounding Interval Envelope
Return minimum=max(0,rounded-resolution/2) and maximum=rounded+resolution/2, requiring nonnegative rounded standard deviation and positive resolution.