Theil Index Calculator
Sample Theil Tinequality using actual nonnegative incomes; zero contributes limiting0log0, all-zero sample undefined. Not a protected-group assessment or sampling-adjusted population estimate.
Description
The Theil T index summarizes inequality relative to a sample's mean income.
The Theil T index summarizes inequality relative to a sample's mean income.1
Its logarithmic terms use a defined zero-income convention and require a positive sample total.
When to use Theil Index Calculator
Use this tool to obtain observedTheilT from the supplied records using the stated calculation. Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
How to use Theil Index Calculator and understand its results
- Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
- Enter observedCompatibleIncomes, using the field meanings and rules below, then run the tool.
- Read result.observedTheilT. Use the units and sign conventions below, and review any unknown records separately.
- Correct any reported input issue and run again. Before using a successful result, check the stated units, signs, reference scope and observation coverage.
| Input field | Meaning | Value type | Requirement |
|---|---|---|---|
| observedCompatibleIncomes | Observed compatible incomes | list of number | Required |
Require a nonempty nonnegative income sample with positive total income. Compute its arithmetic mean and average (income/mean) times natural log(income/mean). A zero income contributes zero by convention; an all-zero sample fails. No sample weights or finite-sample correction are applied.
TheilT=mean((income_i/meanIncome)×ln(income_i/meanIncome)), using zero contribution when income_i=0 Use the matching field units and the exact boundary, ordering and reference rules above.
| Output field | Meaning | Value type |
|---|---|---|
| result | Calculated observation or qualified reference | object |
| result.observedTheilT | Unweighted mean of income/mean times its natural logarithm, with zero-income contributions set to zero. | number |
{
"input": {
"observedCompatibleIncomes": [
0,
2
]
},
"output": {
"result": {
"observedTheilT": 0.6931471805599453
}
}
}Limitations and assumptions
Population definitions, survey design, calibration and observation coverage are independently established. A result describes the supplied record or conditional model without demonstrating causation, validating an instrument or supplying representative population evidence.
Missing required fields, unknown fields, wrong types and violated rules return input issues. Numeric values and outputs must be finite. Lists and matrices must be dense, without missing cells. Numeric lists allow at most 10000 entries, subject to the narrower lengths and code rules above. Extremely large composite outputs are rejected.
Alternative or Complementary methods
For a related step, use Reynolds-Smolensky Redistribution Effect Calculator: The Reynolds–Smolensky comparison subtracts post-tax inequality from pre-tax inequality. For a complementary comparison, use Atkinson Index Calculator: The Atkinson index compares mean income with an equally distributed equivalent under a chosen inequality-aversion parameter.
References
-
Theil Index Calculator — tool.io
Similar or alternative tools
- Reynolds-Smolensky Redistribution Effect Calculator
The Reynolds–Smolensky comparison subtracts post-tax inequality from pre-tax inequality.
- Atkinson Index Calculator
The Atkinson index compares mean income with an equally distributed equivalent under a chosen inequality-aversion parameter.