Description
Extract endpoint atoms from an explicitly sorted finite probability distribution; duplicate/unsorted support and nonnormalized masses are rejected.
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.
Extract endpoint atoms from an explicitly sorted finite probability distribution; duplicate/unsorted support and nonnormalized masses are rejected.
When to use this tool
Use Probability: Finite Support Endpoint Mass 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 support, probabilities. Keep parallel arrays aligned. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require nonempty, equally sized support and probability arrays, strictly increasing numeric support, valid probabilities, and an absolute sum-to-one error at most 1e-12. Return the first and last support values and their associated masses inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| support | Support | Required. Array of finite number. Implementation limit: 128 items. |
| probabilities | Probabilities | Required. Array of finite number. Implementation limit: 128 items. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.lowerEndpoint | Lower Endpoint | Calculated result member: number. |
| result.upperEndpoint | Upper Endpoint | Calculated result member: number. |
| result.lowerMass | Lower Mass | Calculated result member: number. |
| result.upperMass | Upper Mass | Calculated result member: number. |
{
"input": {
"support": [
1,
2,
4
],
"probabilities": [
0.2,
0.3,
0.5
]
},
"output": {
"result": {
"lowerEndpoint": 1,
"upperEndpoint": 4,
"lowerMass": 0.2,
"upperMass": 0.5
}
}
}Limitations and assumptions
- Zero-mass entries can remain at the endpoints. These are the endpoints of the supplied array rather than necessarily the smallest and largest outcomes with positive mass.
- Outputs are nested inside result. 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
- Finite Support Mass Residual
Audit supplied candidate finite-support masses without silently normalizing an invalid total.
- Probability: Discrete Cdf Jump Size
Recover a discrete atom probability from one supplied left limit and right-continuous CDF value, enforcing monotonic probability bounds.