Description
Audit supplied candidate finite-support masses without silently normalizing an invalid 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.
Audit supplied candidate finite-support masses without silently normalizing an invalid total.
When to use this tool
Use Finite Support Mass 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 masses. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read sum, residual, exceedsUnit. Inspect exceedsUnit before interpreting the associated values.
Require every supplied mass between zero and one, then return sum, residual=1-sum, and exceedsUnit=(sum>1).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| masses | Masses | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| sum | Sum | Required. Finite number. |
| residual | Signed observed-minus-implied discrepancy under the stated formula. | Required. Finite number. |
| exceedsUnit | Exceeds Unit | Required. Boolean. |
{
"input": {
"masses": [
0.2,
0.3
]
},
"output": {
"sum": 0.5,
"residual": 0.5,
"exceedsUnit": false
}
}Limitations and assumptions
- No normalization or tolerance is applied. Empty masses give sum zero and residual one; event overlap and omitted support are not checked.
- 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: Finite Support Endpoint Mass
Extract endpoint atoms from an explicitly sorted finite probability distribution; duplicate/unsorted support and nonnormalized masses are rejected.
- Binomial Mass Mode Tie Boundary
Return lowerMode=clamp(ceil(a)-1,0,trials), upperMode=min(trials,floor(a)), and tied when a is an integer from one through trials.