heavytails

heavytails implements continuous and discrete heavy-tailed distributions, tail index estimators and diagnostic utilities with NumPy-backed vectorised evaluation. Every density, quantile and sampler is derived from first principles so the code can be read, checked and taught. Survival functions are computed directly rather than as 1 - cdf(x), so they stay accurate far into the tail where the subtraction has lost every significant digit.

Beyond the distribution interface it covers tail index estimation (Hill-family, robust, bias-reduced, threshold-averaged and peaks-over-threshold estimators), parameter fitting by maximum likelihood and method of moments with AIC and BIC comparison, log-log tail and QQ diagnostics, applied extreme value theory (threshold selection with mean residual life and parameter-stability plots, generalized Pareto fitting, return levels, tail-risk measures, actuarial frequency and severity models, streaming estimators), and dependent extremes (elliptical and multivariate Student-t models, tail dependence, Gaussian, Student-t, Gumbel and Galambos copulas, GARCH fitting, the extremal index and declustering). A command-line interface handles sampling, fitting, comparison and benchmarking, and the package ships type annotations with a py.typed marker.

Install

1

pip install heavytails

Package Metadata

  • Current release: 0.6.3
  • Requires Python: >=3.10,<3.14
  • Status: beta

Where It Fits

Use it for research, teaching and simulation in risk, finance, insurance and extreme-value analysis: when a Gaussian assumption is the thing under test, when a tail index or a return level is the quantity of interest, or when a simulation needs samplers whose tails you can trust. It is the distribution layer behind several of the heavy-tail and risk articles on this site.