Description
Subtract log(removedValue) from logSum, divide by count-1 for logMean, and exponentiate for remainingGeometricMean.
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.
Subtract log(removedValue) from logSum, divide by count-1 for logMean, and exponentiate for remainingGeometricMean.
When to use this tool
Use Geometric Mean Log Deletion Term 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 logSum, count, removedValue. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read remainingGeometricMean, logMean. Use the output convention below.
Subtract log(removedValue) from logSum, divide by count-1 for logMean, and exponentiate for remainingGeometricMean. Require count at least two and positive removed value.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| logSum | Log Sum | Required. Finite number. |
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 2. |
| removedValue | Removed Value | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| remainingGeometricMean | Remaining Geometric Mean | Required. Finite number. |
| logMean | Log Mean | Required. Finite number. |
{
"input": {
"logSum": 4.1588830833596715,
"count": 3,
"removedValue": 2
},
"output": {
"remainingGeometricMean": 5.656854249492379,
"logMean": 1.732867951399863
}
}Limitations and assumptions
- LogSum must be the natural-log sum of the intended original sample. Data membership, other positive observations, and summary consistency are not checked; extreme exponential outputs can be out of range.
- 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
- Arithmetic Geometric Mean Gap Two Values
Return arithmetic=(left+right)/2, geometric=sqrt(left)*sqrt(right), and gap=arithmetic-geometric for nonnegative inputs.
- Log Mean Exp Two Value Stability
Calculate log((exp(left)+exp(right))/2) using the larger input as a shift before exponentiation.