Description
Calculate a Bernoulli outcome's signed probability residual.
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.
Calculate a Bernoulli outcome's signed probability residual.
When to use this tool
Use Bernoulli Trial Signed Residual when you already have successObserved, predictedProbability and need to calculate a Bernoulli outcome's signed probability residual.
How to use the tool and how it works
- Enter successObserved, predictedProbability. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read residual. Use the output convention below.
Require predictedProbability in [0,1]; return (successObserved?1:0)-probability.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| successObserved | Success Observed | Required. Boolean. |
| predictedProbability | Predicted Probability | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| residual | Residual | Required. Finite number. |
{
"input": {
"successObserved": true,
"predictedProbability": 0.25
},
"output": {
"residual": 0.75
}
}Limitations and assumptions
- This is one residual, not a calibration, goodness-of-fit or prediction-accuracy assessment.
- 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
- Two Cdf Values Monotonicity Residual
Compare two supplied CDF values at ordered arguments.
- Weighted Second Moment Contribution
Calculate one weighted squared-deviation contribution about a supplied origin.