Description
Check a supplied intersection against the two marginal probabilities' feasible bounds with an explicit absolute tolerance.
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.
Check a supplied intersection against the two marginal probabilities' feasible bounds with an explicit absolute tolerance.
When to use this tool
Use Joint Probability Rounding Feasibility 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 left, right, intersection, tolerance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read feasible, minimum, maximum. Inspect feasible before interpreting the associated values.
For marginal probabilities left and right compute minimum=max(0,left+right-1) and maximum=min(left,right). Return feasible when intersection lies between minimum-tolerance and maximum+tolerance, requiring nonnegative tolerance.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| left | Left | Required. Finite number; minimum 0; maximum 1. |
| right | Right | Required. Finite number; minimum 0; maximum 1. |
| intersection | Intersection | Required. Finite number. |
| tolerance | Nonnegative absolute allowance in the quantity being compared. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| feasible | Whether the stated supplied bounds pass this local check. | Required. Boolean. |
| minimum | Minimum | Required. Finite number. |
| maximum | Maximum | Required. Finite number. |
{
"input": {
"left": 0.5,
"right": 0.5,
"intersection": 0.5,
"tolerance": 0
},
"output": {
"feasible": true,
"minimum": 0,
"maximum": 0.5
}
}Limitations and assumptions
- Intersection itself need not be within zero through one; tolerance can admit values outside the exact probability bounds. No clamping or joint distribution construction occurs.
- 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
- Probability: Two Event Frechet Bound Interval
Return the sharp Frechet bounds on a two-event intersection from its marginals, with no independence assumption.
- Event Independence Product Bound Gap
Require valid marginals and a joint probability within their exact intersection bounds, then return residual=joint-first*second.