Atkinson Index Calculator

Conditional sample Atkinson index for strictly positive incomes and caller nonnegative inequality aversion; geometric caseε=1handled separately. No universal preference parameter or causal distribution inference.

Description

The Atkinson index compares mean income with an equally distributed equivalent under a chosen inequality-aversion parameter.

The Atkinson index compares mean income with an equally distributed equivalent under a chosen inequality-aversion parameter.^[1]

Strictly positive income observations support the declared power or logarithmic convention.

When to use Atkinson Index Calculator

Use this tool to obtain conditionalAtkinsonIndex 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 Atkinson Index Calculator and understand its results

Establish the population, period, variable definitions, sample coverage and independently applicable instrument or calibration.
Enter observedPositiveIncomes, callerInequalityAversion, using the field meanings and rules below, then run the tool.
Read result.conditionalAtkinsonIndex. 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
observedPositiveIncomes	Observed positive incomes	list of number	Required
callerInequalityAversion	Caller inequality aversion	number	Required

Require a nonempty strictly positive income sample and nonnegative inequality-aversion epsilon. At epsilon exactly one use the geometric mean as equally distributed equivalent; otherwise use the corresponding power mean. Return one minus equivalent/mean income. No survey weights are used; nonfinite arithmetic outputs fail.

A=1−EDE/meanIncome; EDE=exp(mean(ln(income))) if epsilon=1, otherwise mean(income^(1−epsilon))^(1/(1−epsilon))

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.conditionalAtkinsonIndex	One minus the epsilon-dependent equally distributed equivalent divided by mean income.	number

json

{
  "input": {
    "observedPositiveIncomes": [
      1,
      4
    ],
    "callerInequalityAversion": 1
  },
  "output": {
    "result": {
      "conditionalAtkinsonIndex": 0.19999999999999996
    }
  }
}

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 Theil Index Calculator: The Theil T index summarizes inequality relative to a sample's mean income. For a complementary comparison, use Reynolds-Smolensky Redistribution Effect Calculator: The Reynolds–Smolensky comparison subtracts post-tax inequality from pre-tax inequality.

References

Atkinson Index Calculator — tool.io

Similar or alternative tools

Theil Index Calculator
The Theil T index summarizes inequality relative to a sample's mean income.
Reynolds-Smolensky Redistribution Effect Calculator
The Reynolds–Smolensky comparison subtracts post-tax inequality from pre-tax inequality.