Description
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.
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.
Distinguish P(X<t) from P(X<=t) using supplied left-limit and endpoint CDF values.
When to use this tool
Use Censored Event Boundary 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 cdfBefore, cdfAt, inclusive. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read eventProbability, boundaryMass. Use the output convention below.
For cdfBefore<=cdfAt within zero through one return eventProbability=cdfAt when inclusive, otherwise cdfBefore; return boundaryMass=cdfAt-cdfBefore.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| cdfBefore | Cdf Before | Required. Finite number; minimum 0; maximum 1. |
| cdfAt | Cdf At | Required. Finite number; minimum 0; maximum 1. |
| inclusive | Inclusive | Required. Boolean. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| eventProbability | Event Probability | Required. Finite number. |
| boundaryMass | Boundary Mass | Required. Finite number. |
{
"input": {
"cdfBefore": 0.3,
"cdfAt": 0.5,
"inclusive": true
},
"output": {
"eventProbability": 0.5,
"boundaryMass": 0.2
}
}Limitations and assumptions
- These inputs must be a CDF's left limit and value at the same threshold. The result selects an endpoint convention without reconstructing censored observations or estimating a CDF.
- 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
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