Quantile-Based Inequality Indicators for Complex Survey Data.

inequantiles

inequantiles is an R package for estimating quantile-based inequality indicators from survey microdata, with full support for complex sampling designs and weighted quantile estimation.

📖 Documentation and vignette: silviascarpa.github.io/inequantiles

Features

• Quantile ratio index (QRI): estimation from survey data, parametric distributions, and grouped data
• Traditional quantile-based inequality indicators: quantile-based share ratios (e.g., quintile share ratio and Palma index), percentile ratios (e.g., P90/P10)
• Weighted quantile estimation: multiple interpolation rules (types 4–9 and Harrell-Davis) for complex survey data
• Influence functions: linearization-based techniques for QRI, quantiles, quantile-based share ratios, percentile ratios and Gini
• Grouped data: quantiles, QRI and Gini from frequency tables (e.g., fiscal/administrative data)
• Variance estimation: rescaled bootstrap for complex sampling designs

Installation

# install.packages("devtools")
devtools::install_github("silviascarpa/inequantiles")

Quick Start

library(inequantiles)
data(synthouse)

# Weighted quantiles
csquantile(y       = synthouse$eq_income,
           weights = synthouse$weight,
           probs   = c(0.25, 0.5, 0.75),
           type    = 6)

# Quantile ratio index
qri(y       = synthouse$eq_income,
    weights = synthouse$weight)

# All indicators at once
inequantiles(y          = synthouse$eq_income,
             weights    = synthouse$weight,
             indicators = "all")

# Inequality curve
plot_inequality_curve(y       = synthouse$eq_income,
                      weights = synthouse$weight,
                      main    = "Inequality curve — synthouse")

Variance Estimation

Standard errors for all indicators can be estimated simultaneously via the rescaled bootstrap, using a single bootstrap loop for directly comparable results:

inequantiles(
  y          = synthouse$eq_income,
  weights    = synthouse$weight,
  indicators = "all",
  se         = TRUE,
  data       = synthouse,
  strata     = "NUTS2",
  psu        = "municipality",
  B          = 200,
  seed       = 42
)

For custom estimators or more control over the bootstrap, use rescaled_bootstrap() directly.

Influence Functions

Influence functions measure how much each observation affects an estimate — useful for analytical variance estimation and diagnosing influential observations.

# Influence function for the QRI
if_qri(y       = synthouse$eq_income,
       weights = synthouse$weight)

# Influence function for the QSR
if_share_ratio(y       = synthouse$eq_income,
       weights = synthouse$weight,
       prob_numerator = 0.80, prob_denominator = 0.20)

# Influence function for the Gini coefficient
if_gini(y       = synthouse$eq_income,
        weights = synthouse$weight)

# Influence function for the median
if_quantile(y       = synthouse$eq_income,
            weights = synthouse$weight,
            probs   = 0.5)
            
# Influence function for P90/P10
if_ratio_quantiles(y       = synthouse$eq_income,
       weights = synthouse$weight,
       prob_numerator = 0.90, prob_denominator = 0.10
       )

Grouped Data

When only frequency tables are available (e.g., tax records):

income_freq  <- c(120, 180, 150, 80, 40, 20, 10)
income_tot   <- c(18800, 16300, 44700, 33900, 21500, 22100, 98300)
income_lower <- c(0, 15000, 30000, 45000, 60000, 80000, 100000)
income_upper <- c(15000, 30000, 45000, 60000, 80000, 100000, 150000)

quantile_grouped(freq = income_freq,
                 lower_bounds = income_lower,
                 upper_bounds = income_upper,
                 probs = c(0.25, 0.5, 0.75))

qri_grouped(freq = income_freq,
            lower_bounds = income_lower,
            upper_bounds = income_upper)

gini_grouped(Y = income_tot, freq = income_freq)

Citation

If you use inequantiles in your research, please cite:

Scarpa, S. and Sperlich S. (2025). inequantiles: Quantile-Based Inequality Measures for Survey Data. R package. https://github.com/silviascarpa/inequantiles

Getting Help

• 📋 Open an issue
• 📧 [email protected].