Description
Require valid marginals and a joint probability within their exact intersection bounds, then return residual=joint-first*second.
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.
Require valid marginals and a joint probability within their exact intersection bounds, then return residual=joint-first*second.
When to use this tool
Use Event Independence Product Bound Gap 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 first, second, joint. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Require valid marginals and a joint probability within their exact intersection bounds, then return residual=joint-first*second.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| first | First | Required. Finite number; minimum 0; maximum 1. |
| second | Second | Required. Finite number; minimum 0; maximum 1. |
| joint | Joint | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Signed observed-minus-implied discrepancy under the stated formula. | Required. Finite number. |
{
"input": {
"first": 0.5,
"second": 0.5,
"joint": 0.4
},
"output": {
"residual": 0.15000000000000002
}
}Limitations and assumptions
- A zero residual is one supplied two-event independence identity. No sampling uncertainty, tolerance, or broader collection of independence conditions is evaluated.
- 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.
- Censored Event Boundary Mass
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.