Description
Return zero-based Type-7 linear quantile indexes and interpolation fraction.
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 zero-based Type-7 linear quantile indexes and interpolation fraction.
When to use this tool
Use Quantile Interpolation Rank Fraction 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 count, probability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lowerIndex, upperIndex, fraction. Use the output convention below.
Calculate rank=(count-1)*probability and return zero-based lowerIndex, upperIndex, and the fractional interpolation part. Require positive integer count and probability within zero through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| count | Count under the stated input or output convention. | Required. Safe integer; minimum 1. |
| probability | Dimensionless probability from zero through one. | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lowerIndex | Lower Index | Required. Safe integer. |
| upperIndex | Upper Index | Required. Safe integer. |
| fraction | Dimensionless fraction under the stated basis. | Required. Finite number. |
{
"input": {
"count": 6,
"probability": 0.25
},
"output": {
"lowerIndex": 1,
"upperIndex": 2,
"fraction": 0.25
}
}Limitations and assumptions
- This returns indices only under the stated linear convention. No observations are sorted or interpolated, and other quantile rules can select different positions.
- 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
- Sample Quantile Index Fraction Component
Calculate h=(sampleSize-1)*probability and return zero-based floor/ceiling indices and the fractional interpolation part.
- Weighted Quantile Atom Boundary
Weighted empirical inverse using an explicit >= versus > atom-boundary convention, clamped at probability one.