Description
Compare a consistent supplied joint event mass with its independent reference.
Information quantities depend on the logarithm base, event model and symbol accounting. Bits, nats and hartleys are logarithmic units, while source symbols, channel symbols and header bits describe different counting bases. A local mass residual or expansion factor does not estimate entropy, independence or channel capacity from data.
Compare a consistent supplied joint event mass with its independent reference.
When to use this tool
Use Joint Mass Independent Reference Residual when you already have jointMass, firstMarginalMass, secondMarginalMass and need to compare a consistent supplied joint event mass with its independent reference.
How to use the tool and how it works
- Enter jointMass, firstMarginalMass, secondMarginalMass. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read independentReferenceMass, residual. Use the output convention below.
Require marginal masses in [0,1] and joint in [max(0,p+q-1),min(p,q)]; return p*q and joint-p*q.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| jointMass | Joint Mass | Required. Finite number. |
| firstMarginalMass | First Marginal Mass | Required. Finite number; minimum 0; maximum 1. |
| secondMarginalMass | Second Marginal Mass | Required. Finite number; minimum 0; maximum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| independentReferenceMass | Independent Reference Mass | Required. Finite number. |
| residual | jointMass-firstMarginalMass*secondMarginalMass; one joint-cell residual, not an independence significance test. | Required. Finite number. |
{
"input": {
"jointMass": 0.2,
"firstMarginalMass": 0.5,
"secondMarginalMass": 0.3
},
"output": {
"independentReferenceMass": 0.15,
"residual": 0.05000000000000002
}
}Limitations and assumptions
- The masses are supplied rather than estimated. A scalar residual is not a statistical independence test or a complete multivariate distribution analysis.
- 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
Evaluate the full probability model, code and payload/header format when studying information or efficiency. Keep symbol and logarithm bases explicit; a unit conversion or one joint-mass reference term is only a local calculation.
References
Similar or alternative tools
- Information Unit One Bit Reference
Convert a supplied bit quantity to nats and hartleys.
- Brier Reference Class Contribution
Compare predicted and reference single-class squared probability errors.