Description
Weighted empirical inverse using an explicit >= versus > atom-boundary convention, clamped at probability one.
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.
Weighted empirical inverse using an explicit >= versus > atom-boundary convention, clamped at probability one.
When to use this tool
Use Weighted Quantile Atom Boundary 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 values, weights, probability, inclusive. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read value, index, cumulativeWeight. Use the output convention below.
Accumulate positive weights over strictly increasing values until cumulative weight reaches total*probability inclusively or exceeds it exclusively. Return value, zero-based index, and cumulativeWeight; at the upper endpoint retain the last value if no earlier test matches.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| values | Strictly increasing supplied observations with no tied entries. | Required. Array of finite number; maximum items 256. |
| weights | Strictly positive aligned weights. | Required. Array of finite number; maximum items 256. |
| probability | Dimensionless probability from zero through one. | Required. Finite number; minimum 0; maximum 1. |
| inclusive | Inclusive | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| value | Value | Required. Finite number. |
| index | Zero-based index unless the mechanics explicitly state otherwise. | Required. Safe integer. |
| cumulativeWeight | Unnormalized cumulative weight through the selected observation. | Required. Finite number. |
{
"input": {
"values": [
10,
20
],
"weights": [
1,
1
],
"probability": 0.5,
"inclusive": true
},
"output": {
"value": 10,
"index": 0,
"cumulativeWeight": 1
}
}Limitations and assumptions
- Inputs must be aligned, nonempty, and already sorted without ties. No interpolation, tie merging, sorting, or weight interpretation is added; probability zero and one return endpoint observations.
- 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 Quantile Cumulative Boundary Choice
Test whether quantile lies within a supplied cumulative interval: before<quantile<=after with includeEquality, otherwise before<=quantile<after.
- Histogram Bin Boundary Roundoff Policy
Classify value below or above edge, treating values within inclusive absolute tolerance as snapped and assigning them according to preferUpper.