S-Gini (extended Gini family) — iq

Computes the S-Gini coefficient, a one-parameter generalisation of the Gini that allows the user to specify how much weight to give different parts of the distribution. The standard Gini is the special case delta = 2.

Usage

iq_sgini(
  x,
  weights = NULL,
  delta = 2,
  na.rm = FALSE,
  ci = FALSE,
  R = 1000L,
  level = 0.95,
  negatives = c("error", "keep")
)

Arguments

x: Numeric vector of incomes.
weights: Optional numeric vector of survey weights.
delta: Numeric. Inequality aversion parameter (> 1). Default 2 (standard Gini).
na.rm: Logical. Remove NA values? Default FALSE.
ci: Logical. Compute bootstrap confidence intervals? Default FALSE.
R: Integer. Number of bootstrap replicates. Default 1000.
level: Numeric. Confidence level. Default 0.95.
negatives: Character. "error" (default) aborts on negatives; "keep" permits them.

Value

An S3 object of class "iq_sgini" with elements:

value: Numeric. The S-Gini coefficient.
delta: Numeric. The inequality aversion parameter used.
n: Integer. Number of observations.
se, ci_lower, ci_upper, level: Bootstrap CI fields, NULL unless ci = TRUE.
has_negatives: Logical. Whether the input contained negatives.

Details

Lower delta (approaching 1) gives equal weight everywhere; higher delta gives more weight to the bottom of the distribution. The standard Gini (delta = 2) weights by rank position. Delta = 3 or 4 places even more emphasis on the poorest.

Like the standard Gini, the S-Gini is well-defined for distributions containing negative values via negatives = "keep", though the resulting index is no longer bounded in the unit interval.

References

Donaldson, D. and Weymark, J. A. (1980). "A Single-Parameter Generalization of the Gini Indices of Inequality." Journal of Economic Theory, 22(1), 67–86.

Yitzhaki, S. (1983). "On an Extension of the Gini Inequality Index." International Economic Review, 24(3), 617–628.

Examples

d <- iq_sample_data("income")

# Standard Gini (delta = 2)
iq_sgini(d$income, delta = 2)
#> 
#> ── S-Gini (standard Gini, delta = 2) ───────────────────────────────────────────
#> • Value: 0.43
#> • Observations: 1000

# More weight on the bottom of the distribution
iq_sgini(d$income, delta = 3)
#> 
#> ── S-Gini (delta = 3) ──────────────────────────────────────────────────────────
#> • Value: 0.5627
#> • Observations: 1000

# With bootstrap CIs
iq_sgini(d$income, delta = 3, ci = TRUE, R = 200)
#> 
#> ── S-Gini (delta = 3) ──────────────────────────────────────────────────────────
#> • Value: 0.5627
#> • Observations: 1000
#> • Bootstrap 95% CI: [0.539, 0.5859]