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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.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.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.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.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().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.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.README.md with installation instructions, a
quick-start example, a function reference table, and a full Clauset et
al. pipeline walkthrough.NEWS.md (this file).hill_estimator(),
moments_estimator(), pickands_estimator(),
pot_estimator(), plfit(),
doublebootstrap().These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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