Description
Recover a discrete atom probability from one supplied left limit and right-continuous CDF value, enforcing monotonic probability bounds.
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.
Recover a discrete atom probability from one supplied left limit and right-continuous CDF value, enforcing monotonic probability bounds.
When to use this tool
Use Probability: Discrete Cdf Jump Size 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 cdfLeft, cdfAt. 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.
For cdfLeft and cdfAt ordered within zero through one return atomMass=cdfAt-cdfLeft inside result.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cdfLeft | Cdf Left | Required. Finite number. |
| cdfAt | Cdf At | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Object containing the calculated result members described below. | Required. Object. |
| result.atomMass | Atom Mass | Calculated result member: number. |
{
"input": {
"cdfLeft": 0.2,
"cdfAt": 0.5
},
"output": {
"result": {
"atomMass": 0.3
}
}
}Limitations and assumptions
- CdfLeft means the left limit at the same location as cdfAt. Two unrelated CDF observations do not establish an atom at a single point.
- 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
- Discrete Cdf Inverse Flat Step Policy
Find the first cdf entry greater than mass if strict, otherwise greater than or equal to mass.
- Discrete Tail Endpoint Inclusion Term
Return inclusiveTail=strictTail+endpointMass, requiring both inputs within zero through one and their sum no greater than one.