Description
Sum individually valid probabilities into total and return residual=1-total.
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.
Sum individually valid probabilities into total and return residual=1-total.
When to use this tool
Use Probability Partition Exhaustion Residual 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 probabilities. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read total, residual. Use the output convention below.
Sum individually valid probabilities into total and return residual=1-total.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probabilities | Probabilities | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| total | Total | Required. Finite number. |
| residual | Signed observed-minus-implied discrepancy under the stated formula. | Required. Finite number. |
{
"input": {
"probabilities": [
0.25,
0.5
]
},
"output": {
"total": 0.75,
"residual": 0.25
}
}Limitations and assumptions
- A negative residual is allowed and reveals excess mass. Disjointness, coverage, and the identity of the proposed partition are not verified.
- 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
- Atom Probability Lower Slack
For probability and suppliedLowerBound within zero through one return slack=probability-suppliedLowerBound and feasible=(probability>=suppliedLowerBound).
- Conditional Independence One Cell Residual
Require joint, leftGiven, rightGiven, and conditioningMass individually within zero through one; return residual=joint-conditioningMass*leftGiven*rightGiven.