Description
Mark crossed only when lowerPrediction exceeds upperPrediction and return the positive difference, otherwise zero magnitude.
Pinball loss weights underprediction and overprediction differently for a target quantile. Its kink at zero residual requires a subgradient convention, and derivative signs depend on the variable.
Mark crossed only when lowerPrediction exceeds upperPrediction and return the positive difference, otherwise zero magnitude.
When to use this tool
Use Metrics: Quantile Crossing Two Output Flag when you need an explicit quantile-loss term or convention.
How to use the tool and how it works
- Enter lowerQuantile, lowerPrediction, upperQuantile, upperPrediction. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require 0 < lowerQuantile < upperQuantile < 1. Mark crossed only when lowerPrediction exceeds upperPrediction and return the positive difference, otherwise zero magnitude.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lowerQuantile | Lower Quantile | Required. Finite number. |
| lowerPrediction | Lower Prediction | Required. Finite number. |
| upperQuantile | Upper Quantile | Required. Finite number. |
| upperPrediction | Upper Prediction | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.crossed | Crossed | Calculated result member: boolean. |
| result.crossingMagnitude | Crossing Magnitude | Calculated result member: number. |
{
"input": {
"lowerQuantile": 0.1,
"lowerPrediction": 3,
"upperQuantile": 0.9,
"upperPrediction": 2
},
"output": {
"result": {
"crossed": true,
"crossingMagnitude": 1
}
}
}Limitations and assumptions
- Quantile ordering is checked but predictions are not repaired; equality is not classified as crossing.
- Outputs are nested inside result. Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Keep residual definitions consistent and assess quantile calibration and crossing across a complete forecast set.
References
Similar or alternative tools
- Metrics: Pinball Residual Term
For residual defined as actual minus prediction, use quantile × residual when nonnegative and (quantile - 1) × residual otherwise.
- Metrics: Interval Score Observation
Add width, 2/alpha times any shortfall below lower, and 2/alpha times any exceedance above upper.