Description
Return population share, income share, and income share times ln(group mean/global mean), using zero for a zero group mean.
Population and eligibility summaries depend on who enters the numerator and denominator. Weighted shares can differ from unweighted averages, and source coverage is a different property from representativeness or outcome quality.
Return population share, income share, and income share times ln(group mean/global mean), using zero for a zero group mean.
When to use this tool
Use Global Inequality Population Weight Term when you need a population count or share on a declared inclusion basis.
How to use the tool and how it works
- Enter groupPopulation, totalPopulation, groupMeanIncome, globalMeanIncome. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read populationWeight, incomeShare, betweenGroupTheilTerm. Use the output convention below.
Require positive totalPopulation and globalMeanIncome and nonnegative group population within total and nonnegative groupMeanIncome. Return population share, income share, and income share times ln(group mean/global mean), using zero for a zero group mean.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| groupPopulation | Group Population | Required. Finite number; minimum 0. |
| totalPopulation | Total Population | Required. Finite number; strictly above 0. |
| groupMeanIncome | Group Mean Income | Required. Finite number; minimum 0. |
| globalMeanIncome | Global Mean Income | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| populationWeight | Population Weight | Required. Finite number. |
| incomeShare | Income Share | Required. Finite number. |
| betweenGroupTheilTerm | One income-share-weighted natural-log contribution, not a complete Theil index. | Required. Finite number. |
{
"input": {
"groupPopulation": 100,
"totalPopulation": 1000,
"groupMeanIncome": 2000,
"globalMeanIncome": 1000
},
"output": {
"populationWeight": 0.1,
"incomeShare": 0.2,
"betweenGroupTheilTerm": 0.13862943611198905
}
}Limitations and assumptions
- This is one between-group Theil contribution in natural-log units and can be negative; a full decomposition needs compatible groups and means, and no inequality dataset or policy conclusion is verified.
- 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
Reconcile the source population and weighting scheme before comparison. Use a complete statistical analysis when sampling uncertainty, demographic interpretation, or causal explanation matters.
References
Similar or alternative tools
- Global Index Weight Remainder
Sum weights and subtract that sum from targetTotal for remainder.
- Global Index Component Gap
Return their weighted sum, total weight, and publishedIndex minus weighted sum.