Quantile-based inequality indicators

Computes one or more quantile-based inequality indicators simultaneously among QRI, QSR, Palma ratio, and percentile ratio, optionally with standard errors (estimated from the same set of bootstrap replicates), ensuring full comparability across indicators.

Usage

inequantiles(
  y,
  weights = NULL,
  indicators = "all",
  se = FALSE,
  type = 6,
  na.rm = TRUE,
  M = 100,
  prob_num = 0.9,
  prob_den = 0.1,
  B = 200,
  seed = NULL,
  data = NULL,
  strata = NULL,
  psu = NULL,
  N_h = NULL,
  m_h = NULL,
  verbose = TRUE
)

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 four, or any subset of "qri", "qsr", "palma", "ratio_quantiles".

se

Logical; if TRUE, bootstrap standard errors are computed.

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.

prob_num

Numeric in \((0,1)\); numerator quantile for the percentile ratio (default: 0.90). Only used when percentiles ratio is estimated; see ratio_quantiles.

prob_den

Numeric in \((0,1)\); denominator quantile for the percentile ratio (default: 0.10). Only used when percentiles ratio is estimated; see ratio_quantiles.

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.

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.

call

The matched function call.

Details

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

See also

qri, qsr, palma_ratio, ratio_quantiles, rescaled_bootstrap

Other inequality indicators based on quantiles: palma_ratio(), plot_inequality_curve(), qri(), qsr(), ratio_quantiles()

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

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

# Custom percentile ratio (P80/P20 instead of P90/P10)
inequantiles(eq, weights = w, indicators = "ratio_quantiles",
             prob_num = 0.80, prob_den = 0.20)
#> Quantile-based inequality indicators
#> -------------------------------------
#>        Estimate
#> p80p20   3.2411

# \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
#> 
#> Bootstrap replicates: 50
# }