Description
Return [ln(joint) - ln(row) - ln(column)]/ln(base).
Divergences and information densities compare probabilities on a common support. A weighted cell contribution and an unweighted logarithmic ratio differ, and zero-support cases require explicit limits.
Return [ln(joint) - ln(row) - ln(column)]/ln(base).
When to use this tool
Use Information: Information Density Single Joint Cell when you need one precisely defined information-comparison term.
How to use the tool and how it works
- Enter jointProbability, rowProbability, columnProbability, base. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read result. Expand result to inspect the returned fields.
Require positive feasible joint and marginal probabilities and base > 1. Return [ln(joint) - ln(row) - ln(column)]/ln(base).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| jointProbability | Joint Probability | Required. Finite number. |
| rowProbability | Row Probability | Required. Finite number. |
| columnProbability | Column Probability | Required. Finite number. |
| base | Numeric base or source quantity interpreted under the specific calculation above. | Required. Finite number. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| result | Result | Required. Object. |
| result.informationDensity | Unweighted logarithm of joint probability over marginal-product probability. | Calculated result member: number. |
{
"input": {
"jointProbability": 0.25,
"rowProbability": 0.5,
"columnProbability": 0.5,
"base": 2
},
"output": {
"result": {
"informationDensity": 0
}
}
}Limitations and assumptions
- This is unweighted information density, not its joint-probability-weighted contribution or total mutual information.
- Outputs are nested inside result. 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
Align and validate complete distributions before summing terms or interpreting a full divergence or dependence measure.
References
Similar or alternative tools
- Information: Mutual Information Single Cell Term
Validate marginals in [0, 1] and jointProbability between max(0, row + column - 1) and min(row, column).
- Pointwise Log Likelihood Ratio
Return ln(firstProbability/secondProbability)/ln(logBase).