Description
Expose zero likelihood and a contradiction with supplied support membership.
Probability calculations distinguish event mass, density likelihood, support membership and interval inclusion. Zero likelihood is not always proof of impossibility, and a known zero-probability category differs from an absent label. Independence, disjointness and supplied CDF values are assumptions or records, rather than properties established by local arithmetic.
Expose zero likelihood and a contradiction with supplied support membership.
When to use this tool
Use Likelihood Impossible Support Flag when you already have suppliedLikelihood, insideSuppliedSupport and need to expose zero likelihood and a contradiction with supplied support membership.
How to use the tool and how it works
- Enter suppliedLikelihood, insideSuppliedSupport. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read zeroLikelihood, supportContradiction. Inspect zeroLikelihood, supportContradiction before interpreting the associated values.
Require likelihood>=0; zeroLikelihood means exactly zero, and supportContradiction means outside support with nonzero likelihood.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| suppliedLikelihood | Nonnegative likelihood or density value; may exceed one. | Required. Finite number; minimum 0. |
| insideSuppliedSupport | Inside Supplied Support | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| zeroLikelihood | Exact equality to zero, not proof of impossibility. | Required. Boolean. |
| supportContradiction | Support Contradiction | Required. Boolean. |
{
"input": {
"suppliedLikelihood": 0,
"insideSuppliedSupport": false
},
"output": {
"zeroLikelihood": true,
"supportContradiction": false
}
}Limitations and assumptions
- Likelihood may exceed one for a density; zero does not prove impossibility, support is asserted and no model 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. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete joint model when independence or disjointness cannot be assumed. Evaluate a distribution on its actual support for CDF or likelihood questions, and keep absent categories distinct from explicitly listed zero-probability outcomes.
References
Similar or alternative tools
- Categorical Label Probability Lookup
Look up a categorical probability while distinguishing a missing label.
- Bernoulli Trial Signed Residual
Calculate a Bernoulli outcome's signed probability residual.