Source: https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/mechanism/

instrument mechanism / verified-clean

# Gini Coefficient / Lorenz Curve Estimator mechanism

The inspectable method record for Gini Coefficient / Lorenz Curve Estimator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core Gini and trapezoidal Lorenz method is standard, but the specification needs explicit fraction-versus-percent handling, sorting and nonnegative-data constraints, zero-total handling, endpoint requirements, and a clear statement that decile/quintile results are grouped-data estimates. The educational-only honest label is appropriate.

- The formula Gini=A/(A+B) is mathematically correct only when A is the area between the equality line and Lorenz curve and B is the area under the Lorenz curve; the implementation should explicitly use Gini=(0.5-B)/0.5=1-2B because the equality-line area A+B is 0.5.

- The trapezoidal calculation must include the Lorenz endpoints (0,0) and (1,1), and must define B as the sum of trapezoids between consecutive cumulative population and cumulative income/wealth shares.

- The input specification does not state whether shares are entered as fractions or percentages, nor whether decile/quintile groups are assumed to have equal population weights.

- The instrument must require observations to be sorted from lowest to highest income/wealth and must reject negative shares, negative population weights, and distributions whose total income/wealth is zero.

## Units and conventions

- Population shares and income/wealth shares are dimensionless proportions; fractions such as 0.10 are assumed unless an explicit percent-input mode converts 10% to 0.10.

- For deciles, cumulative population coordinates are x=0,0.1,...,1. For quintiles, they are x=0,0.2,...,1.

- Income/wealth shares must sum to exactly 1 after normalization, and population shares must sum to 1.

- The Lorenz curve is piecewise linear between cumulative-share points; the reported Gini is therefore the grouped-data trapezoidal estimate.

- The equality line is y=x, whose area under the curve on [0,1] is 0.5.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "grouping": "10 equal-population deciles",
    "income_shares": [
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1,
      0.1
    ],
    "sampled_x": [
      0,
      0.5,
      1
    ]
  },
  "expected_outputs": {
    "gini": 0,
    "lorenz_sampled_points": [
      {
        "x": 0,
        "y": 0
      },
      {
        "x": 0.5,
        "y": 0.5
      },
      {
        "x": 1,
        "y": 1
      }
    ],
    "curve_features": {
      "equality_intersections": "Every point on 0<=x<=1",
      "maximum_gap_from_equality": 0,
      "asymptotes": "None"
    }
  },
  "working": "Cumulative Lorenz y-values: 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1. Each trapezoid has width 0.1 and average height 0.1. B=10*(0.1*((0.1+0.1)/2))=10*0.01=0.10? Including the endpoint formula directly: B=0.1*(0.5*0+0.1+0.2+0.3+0.4+0.5+0.6+0.7+0.8+0.9+0.5*1)=0.1*(5.0)=0.5. A=0.5-B=0.5-0.5=0. Gini=A/(A+B)=0/0.5=0. The Lorenz curve is y=x, so y(0.5)=0.5 and its maximum gap from equality is 0."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The zero-total input produces an undefined normalization denominator and must be rejected. The specification also does not state how group ordering or percentage-versus-fraction units are interpreted; reversed ordering can yield an invalid negative formal Gini.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/gini-coefficient-lorenz-curve-estimator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche6/tranche6-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`