Description
For probability and suppliedLowerBound within zero through one return slack=probability-suppliedLowerBound and feasible=(probability>=suppliedLowerBound).
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.
For probability and suppliedLowerBound within zero through one return slack=probability-suppliedLowerBound and feasible=(probability>=suppliedLowerBound).
When to use this tool
Use Atom Probability Lower Slack 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 probability, suppliedLowerBound. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read slack, feasible. Inspect feasible before interpreting the associated values.
For probability and suppliedLowerBound within zero through one return slack=probability-suppliedLowerBound and feasible=(probability>=suppliedLowerBound).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Dimensionless probability from zero through one. | Required. Finite number; minimum 0; maximum 1. |
| suppliedLowerBound | Supplied Lower Bound | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| slack | Slack | Required. Finite number. |
| feasible | Whether the stated supplied bounds pass this local check. | Required. Boolean. |
{
"input": {
"probability": 0.3,
"suppliedLowerBound": 0.2
},
"output": {
"slack": 0.09999999999999998,
"feasible": true
}
}Limitations and assumptions
- Feasibility refers only to this supplied lower bound. A negative slack is a successful result rather than a malformed-input error.
- 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
- Conditional Probability Mixture One Component
Multiply weight and conditional, both fractions within zero through one, into jointContribution.
- Conditional Probability Zero Case Label
A positive condition returns conditional=jointProbability/conditionProbability, defined=true, and label=defined; zero condition returns conditional=0, defined=false, and label=undefined-zero-condition.