Description
Return interval width plus a penalty of 2/alpha times the distance below lower or above upper; observations within the interval add no penalty.
An interval forecast has both a width and a relationship to an observed value. Scoring rules can penalize narrow misses while boundary conventions determine coverage separately.
Return interval width plus a penalty of 2/alpha times the distance below lower or above upper; observations within the interval add no penalty.
When to use this tool
Use Winkler Score Width Penalty Split when you need one interval width, coverage, penalty, or error-envelope term.
How to use the tool and how it works
- Enter observed, lower, upper, alpha. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read width, penalty, score. Use the output convention below.
Require lower ≤ upper and alpha in (0, 1). Return interval width plus a penalty of 2/alpha times the distance below lower or above upper; observations within the interval add no penalty.1
For a central prediction interval, alpha is the total nominal probability outside the interval, with alpha/2 in each tail. The interval score combines width with a penalty for observations outside the bounds; lower scores are preferred.2
| Input field | Meaning and units | Accepted input |
|---|---|---|
| observed | Observed | Required. Finite number. |
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| alpha | Nominal interval miscoverage as a fraction, not a percentage. | Required. Finite number; strictly above 0; strictly below 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| width | Width | Required. Finite number. |
| penalty | Penalty | Required. Finite number. |
| score | Score under the explicit mathematical and availability conventions above. | Required. Finite number. |
{
"input": {
"observed": 12,
"lower": 5,
"upper": 10,
"alpha": 0.1
},
"output": {
"width": 5,
"penalty": 40,
"score": 45
}
}Limitations and assumptions
- Alpha is a fractional miscoverage level, not percent; this evaluates one interval rather than calibration or average forecast quality.
- 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
Aggregate scores over comparable observations and examine empirical coverage and interval width together.
References
-
Calculation and input contract: metrics/winkler-score-width-penalty-split — tool.io
-
Strictly Proper Scoring Rules, Prediction, and Estimation — Tilmann Gneiting and Adrian E. Raftery / Journal of the American Statistical Association
Similar or alternative tools
- Metrics: Interval Score Observation
Add width, 2/alpha times any shortfall below lower, and 2/alpha times any exceedance above upper.
- Interval Score Missing Endpoint Case
With both endpoints present, validate their order and calculate width plus scaled outside penalties; otherwise return score zero, defined false, and missing endpoint names.