heavytails 0.2.0

New Functions

Pareto Estimation

• mle_pareto() — Parametric MLE for the Pareto tail index using the closed-form estimator from Theorem 8.1 of Nair et al. Supports an optional finite-sample bias correction (§8.3). Returns a heavytails_mle object with a print() method.
• wls_pareto() — Weighted least-squares estimator for the Pareto tail index via log-log rank regression (Theorem 8.5 of Nair et al.). Optionally draws the rank plot with both WLS and OLS fitted lines. Also returns the unweighted OLS estimate for comparison.
• ks_xmin() — Standalone KS-minimization estimator for the power-law lower bound x̂_m (Step 1 of the Clauset et al. pipeline, §8.5). Extracts the core loop from plfit() so x̂_m can be estimated without running the full power-law fit.

Goodness-of-Fit

• ks_gof() — Bootstrap Kolmogorov-Smirnov goodness-of-fit test for the Pareto distribution (Step 2 of the Clauset et al. pipeline, §8.5). The p-value is the fraction of parametric bootstrap KS statistics exceeding the observed statistic.
• lr_test_pareto() — Vuong likelihood-ratio test comparing the Pareto fit against alternative distributions: "exponential", "lognormal", and "weibull" (Step 3 of the Clauset et al. pipeline; Clauset et al. 2009, §3.3). Returns a data.frame with the LR statistic, two-sided p-value, and preferred model for each alternative.

Visual Diagnostics

• hill_plot() — Hill plot: α̂ vs. k over a range of tail sizes. Accepts an optional alpha_true argument to overlay the true value as a reference line (useful in simulation studies). Returns the plotted data.frame invisibly.
• moments_plot() — Moments estimator plot: ξ̂ vs. k. Returns the plotted data.frame invisibly.
• pickands_plot() — Pickands estimator plot: ξ̂ vs. k. Returns the plotted data.frame invisibly.
• rank_plot() — Log-rank vs. log-x plot for assessing Pareto linearity. Returns the plotted data.frame invisibly.
• qq_pareto() — Pareto Q-Q plot. Accepts an optional alpha argument; if omitted, mle_pareto() is called internally on the data. Returns the theoretical and empirical quantiles invisibly.

Pareto Utilities (newly exported)

• rpareto() — Generate Pareto(xm, α) random variates. Promoted from internal helper to exported function.
• pareto_cdf() — Pareto CDF. Promoted from internal helper to exported function.
• dpareto() — Pareto density function. New function.

Bug Fixes

• Hill estimator indexing corrected. The denominator in the Hill formula was X_(k) instead of X_(k+1), causing the k-th term in the average to always be zero and biasing the estimate upward. The formula now correctly divides by X_(k+1), consistent with Eq. 9.12 of Nair et al. and the internal db_estimators() helper used by doublebootstrap().
• Dead code removed from doublebootstrap(). The if (n2 < 5) check was unreachable because the preceding if (n2 <= 5) already covered that case. The if (n1 != -1 && n1 >= n) check was also unreachable because n1 had already been overwritten from its -1 default earlier in the function body. Both branches have been removed.

Breaking Changes

• gpd_lg_likelihood() is no longer exported. It is an internal optimization helper for pot_estimator() and was never intended for direct use. Any code calling gpd_lg_likelihood() directly should switch to heavytails:::gpd_lg_likelihood() or, preferably, use pot_estimator() instead.

Documentation

• Added README.md with installation instructions, a quick-start example, a function reference table, and a full Clauset et al. pipeline walkthrough.
• All new functions have full roxygen2 documentation with LaTeX math, parameter descriptions, return value specifications, examples, and references to Nair et al. (2022) and Clauset et al. (2009).
• Added NEWS.md (this file).

heavytails 0.1.0

• Initial CRAN release.
• Implemented tail index estimators: hill_estimator(), moments_estimator(), pickands_estimator(), pot_estimator(), plfit(), doublebootstrap().