Description
Transform a closed probability-uncertainty interval through the decreasing complement map, reversing endpoints.
Event probabilities and probability masses lie between zero and one. Marginals, intersections, conditioning events, and endpoint atoms describe different quantities. A probability bound or local consistency check can constrain a model without specifying its complete distribution or dependence structure.
Transform a closed probability-uncertainty interval through the decreasing complement map, reversing endpoints.
When to use this tool
Use Probability: Event Complement Interval Bounds when you need the stated event identity, boundary policy, distribution component, or local feasibility check.
How to use the tool and how it works
- Enter lowerProbability, upperProbability. 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.
For ordered lowerProbability and upperProbability within zero through one return complementLower=1-upperProbability and complementUpper=1-lowerProbability inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lowerProbability | Lower Probability | Required. Finite number. |
| upperProbability | Upper Probability | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.complementLower | Complement Lower | Calculated result member: number. |
| result.complementUpper | Complement Upper | Calculated result member: number. |
{
"input": {
"lowerProbability": 0.2,
"upperProbability": 0.7
},
"output": {
"result": {
"complementLower": 0.3,
"complementUpper": 0.8
}
}
}Limitations and assumptions
- Only numeric probability bounds are transformed. Endpoint openness and dependence between other constraints are not represented.
- 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. Signed zero is exported as zero.
Alternative or Complementary methods
Use a full probability table or distribution when a local mass, bound, or identity is insufficient. Specify dependence, conditioning, support order, and endpoint policy before combining terms.
References
Similar or alternative tools
- Conditional Event Complement Gap
Return conditionalProbability=jointProbability/conditioningProbability, impliedComplement=1-conditionalProbability, and gap=suppliedComplement-impliedComplement.
- Hazard To Discrete Event One Interval
For nonnegative hazard and duration return probability=-expm1(-hazard*duration).