Quantile-based inequality indicators

Estimates one or more quantile-based inequality indicators simultaneously — QRI, quantile-based share ratio (QSR, Palma, or custom), percentile ratio — together with the Gini coefficient as a widely used benchmark. When standard errors are requested, all indicators are evaluated on the same bootstrap replicates, ensuring full comparability.

Usage

inequantiles(
  y,
  weights = NULL,
  indicators = "all",
  se = FALSE,
  type = 6,
  na.rm = TRUE,
  M = 100,
  B = 200,
  seed = NULL,
  data = NULL,
  strata = NULL,
  psu = NULL,
  N_h = NULL,
  m_h = NULL,
  verbose = TRUE
)

# S3 method for class 'inequantiles'
print(x, digits = 4, ...)

Arguments

y

A numeric vector of strictly positive values (e.g. income, wealth, expenditure).

weights

A numeric vector of sampling weights. If NULL, all observations are equally weighted.

indicators

Character vector specifying which indicators to compute. Use "all" (default) for all, or any subset of "qri", "qsr", "palma", "ratio_quantiles", "gini". "qsr" (quintile share ratio) and "palma" (Palma index) are special cases of share_ratio. "ratio_quantiles" computes the P90/P10.

se

Logical; if TRUE, standard errors are estimated via the rescaled bootstrap; see rescaled_bootstrap. Requires data and strata (see below).

type

Quantile estimation type: integer 4–9 or "HD" for Harrell–Davis (default: 6). See csquantile.

na.rm

Logical; remove missing values before computing? Default: TRUE.

M

Integer; number of quantile-ratio grid points for the QRI (default: 100). Only used when the QRI is estimated; see qri.

B

Integer; number of bootstrap replicates (default: 200). Only used when se = TRUE.

seed

Integer; random seed for reproducibility. Only used when se = TRUE.

data

A data frame containing the survey design variables (strata, PSU). Required when se = TRUE.

strata

Character string; name of the stratification column in data. Required when se = TRUE.

psu

Character string; name of the PSU column in data. Required for two-stage complex designs.

N_h

Optional named numeric vector of stratum population sizes for the finite population correction. See rescaled_bootstrap.

m_h

Optional vector of bootstrap sample sizes per stratum. Defaults to the Rao-Wu formula. See rescaled_bootstrap.

verbose

Logical; if TRUE (default), displays a progress bar during bootstrap iterations.

x

An object of class "inequantiles".

digits

Integer; number of decimal places for rounding (default: 4).

...

Further arguments passed to or from other methods.

Value

A list with components:

estimates

Numeric vector of point estimates of inequality indicators.

se

Numeric vector of standard errors, or NULL when se = FALSE.

B

Number of bootstrap replicates used, or NULL.

design

Sampling design type detected by the bootstrap, or NULL when se = FALSE.

call

The matched function call.

The argument x, invisibly.

Details

All quantile-based indicators are computed from the same specified csquantile type. When se = TRUE, a single bootstrap loop is run through the rescaled bootstrap method (see rescaled_bootstrap) and all indicators are evaluated on each replicate, so standard errors are based on identical resamples and are directly comparable.

The Gini coefficient is estimated following (Langel and Tillé 2013) , equation 6, using a weighted formula based on cumulative weight sums.

See also

qri, share_ratio, ratio_quantiles, rescaled_bootstrap

Other inequality indicators based on quantiles: plot_inequality_curve(), qri(), ratio_quantiles(), share_ratio(), superpop_qri()

Examples

data(synthouse)
eq <- synthouse$eq_income
w  <- synthouse$weight

# Point estimates only
inequantiles(eq, weights = w)
#> Quantile-based inequality indicators
#> -------------------------------------
#>        Estimate
#> qri      0.5691
#> qsr      7.0161
#> palma    1.5787
#> p90p10   5.9206
#> gini     0.3715

# Subset of indicators
inequantiles(eq, weights = w, indicators = c("qri", "palma"))
#> Quantile-based inequality indicators
#> -------------------------------------
#>       Estimate
#> qri     0.5691
#> palma   1.5787


# \donttest{
# With bootstrap standard errors (complex design)
inequantiles(eq, weights = w,
             se = TRUE, B = 50, seed = 42,
             data = synthouse, strata = "NUTS2",
             psu = "municipality",
             verbose = FALSE)
#> Quantile-based inequality indicators
#> -------------------------------------
#>        Estimate     SE
#> qri      0.5691 0.0046
#> qsr      7.0161 0.1757
#> palma    1.5787 0.0387
#> p90p10   5.9206 0.1638
#> gini     0.3715 0.0043
#> 
#> Bootstrap replicates: 50
# }