Description
For nonnegative hazard and duration return probability=-expm1(-hazard*duration).
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.
For nonnegative hazard and duration return probability=-expm1(-hazard*duration).
When to use this tool
Use Hazard To Discrete Event One Interval 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 hazard, duration. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read probability. Use the output convention below.
For nonnegative hazard and duration return probability=-expm1(-hazard*duration).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| hazard | Nonnegative constant hazard in inverse duration units. | Required. Finite number; minimum 0. |
| duration | Nonnegative interval duration in the matching time unit. | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| probability | Dimensionless probability from zero through one. | Required. Finite number. |
{
"input": {
"hazard": 0.6931471805599453,
"duration": 1
},
"output": {
"probability": 0.5
}
}Limitations and assumptions
- Hazard has reciprocal-time units and duration must use the matching time unit. The expression assumes a constant hazard over the interval; it does not fit a time-varying survival model.
- 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
- Probability: Event Complement Interval Bounds
Transform a closed probability-uncertainty interval through the decreasing complement map, reversing endpoints.
- Probability: Two Event Frechet Bound Interval
Return the sharp Frechet bounds on a two-event intersection from its marginals, with no independence assumption.