Description
Return skewness=thirdCentralMoment/variance^1.5, requiring positive variance.
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 skewness=thirdCentralMoment/variance^1.5, requiring positive variance.
When to use this tool
Use Skewness Standardization Scale Factor 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 thirdCentralMoment, variance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read skewness. Use the output convention below.
Return skewness=thirdCentralMoment/variance^1.5, requiring positive variance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| thirdCentralMoment | Third Central Moment | Required. Finite number. |
| variance | Variance | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| skewness | Skewness | Required. Finite number. |
{
"input": {
"thirdCentralMoment": 16,
"variance": 4
},
"output": {
"skewness": 2
}
}Limitations and assumptions
- Moment and variance must share a consistent population or weighting basis. No data are summarized, no finite-sample skewness correction is applied, and zero-variance input is rejected.
- 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.
- Arithmetic Geometric Mean Gap Two Values
Return arithmetic=(left+right)/2, geometric=sqrt(left)*sqrt(right), and gap=arithmetic-geometric for nonnegative inputs.