Description
Check overlap of two closed probability intervals.
Probability calculations distinguish event mass, density likelihood, support membership and interval inclusion. Zero likelihood is not always proof of impossibility, and a known zero-probability category differs from an absent label. Independence, disjointness and supplied CDF values are assumptions or records, rather than properties established by local arithmetic.
Check overlap of two closed probability intervals.
When to use this tool
Use Probability Interval Rounding Overlap when you already have firstLower, firstUpper, secondLower, secondUpper and need to check overlap of two closed probability intervals.
How to use the tool and how it works
- Enter firstLower, firstUpper, secondLower, secondUpper. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read overlap, intersectionLower, intersectionUpper. Inspect overlap before interpreting the associated values.
Require each interval ordered within [0,1]; overlap means max(lowers)<=min(uppers). Return those intersection bounds even when disjoint.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstLower | First Lower | Required. Finite number; minimum 0; maximum 1. |
| firstUpper | First Upper | Required. Finite number; maximum 1. |
| secondLower | Second Lower | Required. Finite number; minimum 0; maximum 1. |
| secondUpper | Second Upper | Required. Finite number; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| overlap | Overlap | Required. Boolean. |
| intersectionLower | max(lower endpoints), even when it exceeds intersectionUpper for disjoint intervals. | Required. Finite number. |
| intersectionUpper | Intersection Upper | Required. Finite number. |
{
"input": {
"firstLower": 0.2,
"firstUpper": 0.4,
"secondLower": 0.3,
"secondUpper": 0.5
},
"output": {
"overlap": true,
"intersectionLower": 0.3,
"intersectionUpper": 0.4
}
}Limitations and assumptions
- Touching endpoints overlap; when disjoint, lower exceeds upper and the pair is not a valid intersection interval. No rounding policy or confidence level is inferred.
- 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
Use the complete joint model when independence or disjointness cannot be assumed. Evaluate a distribution on its actual support for CDF or likelihood questions, and keep absent categories distinct from explicitly listed zero-probability outcomes.
References
Similar or alternative tools
- QC Spec Limit Inclusion Policy
Check a result against supplied limits with independent endpoint inclusion.
- Finite Event Mass Remaining Budget
Calculate unassigned probability mass after supplied disjoint event masses.