Description
Require mass in [0, 1] and positive order, then return mass^order.
Entropy summarizes uncertainty under a specified probability model and logarithm convention. Support indicators, one-symbol terms, and exponentiated entropies are components with different meanings.
Require mass in [0, 1] and positive order, then return mass^order.
When to use this tool
Use Rényi Power Sum One Symbol Term when you need one explicitly scoped entropy or support calculation.
How to use the tool and how it works
- Enter mass, order. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read term. Use the output convention below.
Require mass in [0, 1] and positive order, then return mass^order.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| mass | Probability mass, dimensionless, in the stated domain. | Required. Finite number; minimum 0; maximum 1. |
| order | Order parameter for the stated entropy-family term. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| term | Single mathematical contribution; aggregation and normalization are separate. | Required. Finite number. |
json
{
"input": {
"mass": 0.5,
"order": 2
},
"output": {
"term": 0.25
}
}Limitations and assumptions
- This is one Rényi power-sum contribution, not entropy itself; aggregation, logarithm, and the order-one limit are separate.
- 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
- Tsallis Entropy One Symbol Term
Return (mass - mass^order)/(order - 1).
- Collision Probability Single Symbol Term
Validate probability in [0, 1] and square it for contribution.