Description
Return -1/[probability × (1 - probability) × ln(logBase)].
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
Return -1/[probability × (1 - probability) × ln(logBase)].
When to use this tool
Use Binary Entropy Curvature Term when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter probability, logBase. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read curvature. Use the output convention below.
Require probability in (0, 1) and positive logBase different from one. Return -1/[probability × (1 - probability) × ln(logBase)].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| probability | Probability in the stated interval; zero handling follows the calculation above. | Required. Finite number; strictly above 0; strictly below 1. |
| logBase | Logarithm base; base 2 gives bits and base e gives nats under conventional bases greater than one. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| curvature | Curvature | Required. Finite number. |
{
"input": {
"probability": 0.5,
"logBase": 2.718281828459045
},
"output": {
"curvature": -4
}
}Limitations and assumptions
- Bases below one reverse the usual curvature sign; this is a derivative term rather than an entropy estimate.
- 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
Validate and align complete probability distributions before aggregating terms or interpreting an uncertainty estimate.
References
Similar or alternative tools
- Binary Entropy Second Input Derivative
Return -1/[ln(2) × probability × (1 - probability)] for probability strictly inside (0, 1).
- Entropy Base Ratio
Return ln(sourceBase)/ln(targetBase) for positive bases different from one.