Description
Return the sharp Frechet bounds on a two-event intersection from its marginals, with no independence assumption.
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.
Return the sharp Frechet bounds on a two-event intersection from its marginals, with no independence assumption.
When to use this tool
Use Probability: Two Event Frechet Bound Interval 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 pA, pB. 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.
Return lower=max(0,pA+pB-1) and upper=min(pA,pB) inside result, requiring both marginal probabilities within zero through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| pA | P A | Required. Finite number. |
| pB | P B | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.lower | Lower | Calculated result member: number. |
| result.upper | Upper | Calculated result member: number. |
{
"input": {
"pA": 0.8,
"pB": 0.6
},
"output": {
"result": {
"lower": 0.4,
"upper": 0.6
}
}
}Limitations and assumptions
- These intersection bounds impose no independence assumption and do not select the actual joint probability.
- 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
- Joint Probability Rounding Feasibility
Check a supplied intersection against the two marginal probabilities' feasible bounds with an explicit absolute tolerance.
- Event Union Disjointness Correction
For valid marginal probabilities and an intersection within their exact feasible bounds, return union=left+right-intersection and correction=-intersection.