inequality

iq_palma(), iq_hoover(), iq_kolm(), iq_percentile_ratio(),

iq_polarisation(), iq_shares(), iq_concentration(), iq_kakwani(),

and iq_poverty().

The bootstrap uses probability-proportional resampling, so survey weights

flow through to the variance, not just the point estimate.

iq_compare() runs one bootstrap loop, propagates CIs to every row

When ci = TRUE, iq_compare() now runs a single resample loop and

attaches ci_lower and ci_upper columns to every row of the table. The

old gini_ci field is removed. The table now also covers S-Gini,

Kolm, and Wolfson (12 measures, up from 9).

Negative values are now supported via negatives = "keep"

Functions that are mathematically defined for distributions containing

negative values now accept negatives = c("error", "keep"), with

"error" as the default for back-compatibility. With negatives = "keep":

• iq_gini() and iq_sgini() permit negatives; the index is still computed by the standard formula but is no longer bounded in [0, 1]. The print method emits a note when the input contains negatives.
• iq_shares() permits negatives; segment shares may fall outside [0, 1] and a warning is issued. If total income is non-positive, the function returns NA shares with a warning.
• iq_palma(), iq_hoover(), and iq_polarisation() similarly accept negatives.

iq_kolm() already worked for negative values and is unchanged.

iq_atkinson() and iq_theil() continue to require strictly positive

values: they involve log(x) or x^(1 - epsilon) for which the formula

is mathematically undefined at zero or below. The error message now

documents this explicitly.

Bug fixes

• iq_kakwani() no longer takes the absolute value of post-tax income before computing the post-tax Gini. Households whose post-tax income is negative are now reflected honestly in the Reynolds-Smolensky index.
• iq_palma() and iq_polarisation() now warn rather than abort when the relevant denominator is non-positive (returning NA).
• The standard Gini now returns NA (with a warning) when the population mean is non-positive. Previously the function returned 0 when mu == 0, which conflated "perfect equality" with "undefined". With negatives = "keep" set, the user is pointed at normalised = TRUE for the Raffinetti et al. (2017) bounded variant.
• The Watts poverty index drops observations with x = 0 from the Watts sum (since log(line / 0) diverges) and emits a one-time warning. FGT measures and the Sen index continue to include all poor observations.
• iq_percentile_ratio() now warns when the lower percentile is negative, since the resulting ratio sign-flips and has no inequality interpretation.
• The error message for measures that require strictly positive input (Theil, Atkinson, decompose, growth_incidence) no longer suggests setting negatives = "keep", which those wrappers do not expose. Instead the message points the user at measures that admit zero or negative support.

New features (audit follow-up)

• iq_gini() gains a normalised flag implementing the Raffinetti, Siletti and Vernizzi (2017) Gini variant, which is bounded in [-1, 1] for distributions containing negative values.
• iq_compare() gains a negatives argument. With negatives = "keep" it permits zero or negative input and returns NA for the Theil and Atkinson rows (which are mathematically undefined for non-positive values), while still computing Gini, S-Gini, Kolm, Wolfson, Hoover, Palma and percentile-ratio rows.
• iq_concentration() gains a correction = "wagstaff" option for the Wagstaff (2005) normalised concentration index, alongside the existing Erreygers (2009) correction.
• ?iq_theil now documents the convention difference vs the legacy ineq package (ineq::Theil(x, parameter = 0) corresponds to GE(1) / Theil T here, not to GE(0) / Theil L).
• New tests/testthat/test-axioms.R locks in scale invariance, Kolm translation invariance, Pigou-Dalton transfer principle, anonymity, parameter monotonicity, decomposition exactness, the Erreygers and Wagstaff bounds, and bootstrap nominal coverage.
• New tests/testthat/test-cross-package.R cross-checks Gini, Theil, and Atkinson values against the legacy ineq package on a fixed seed. Skipped when ineq is not installed and on CRAN.

Acknowledgements

Thanks to Frank Cowell and Emmanuel Flachaire for the careful read and

the two-line list of gaps.