Description
Map a probability interval [lower,upper] to complement bounds 1-upper and 1-lower, swapping the corresponding lowerClosed and upperClosed flags.
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.
Map a probability interval [lower,upper] to complement bounds 1-upper and 1-lower, swapping the corresponding lowerClosed and upperClosed flags.
When to use this tool
Use Probability Bound Complement Open Closed 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 lower, upper, lowerClosed, upperClosed. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read lower, upper, lowerClosed, upperClosed. Inspect lowerClosed, upperClosed before interpreting the associated values.
Map a probability interval [lower,upper] to complement bounds 1-upper and 1-lower, swapping the corresponding lowerClosed and upperClosed flags. Require ordered bounds within zero through one.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| lower | Lower | Required. Finite number; minimum 0; maximum 1. |
| upper | Upper | Required. Finite number; minimum 0; maximum 1. |
| lowerClosed | Whether the lower endpoint belongs to the interval; output inherits the input upper flag. | Required. Boolean. |
| upperClosed | Whether the upper endpoint belongs to the interval; output inherits the input lower flag. | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| lower | Lower | Required. Finite number. |
| upper | Upper | Required. Finite number. |
| lowerClosed | Whether the lower endpoint belongs to the interval; output inherits the input upper flag. | Required. Boolean. |
| upperClosed | Whether the upper endpoint belongs to the interval; output inherits the input lower flag. | Required. Boolean. |
{
"input": {
"lower": 0.25,
"upper": 0.5,
"lowerClosed": true,
"upperClosed": false
},
"output": {
"lower": 0.5,
"upper": 0.75,
"lowerClosed": false,
"upperClosed": true
}
}Limitations and assumptions
- Equal bounds with an open endpoint can denote an empty interval; the tool preserves the supplied endpoint policy rather than rejecting that case.
- 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 Event Complement Gap
Return conditionalProbability=jointProbability/conditioningProbability, impliedComplement=1-conditionalProbability, and gap=suppliedComplement-impliedComplement.