Empirical Distribution

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Summary

Adds EmpiricalDistribution — a continuous univariate distribution built from observed data via a pluggable density estimator (KDE by default). PDF is provided analytically; CDF and PPF are derived automatically by the characteristic graph.

See examples/example_empirical_distribution.ipynb for end-to-end usage.

Added

Distribution

• EmpiricalDistribution — wraps any EmpiricalMethod into a Distribution
• EmpiricalMethod / FittedEmpirical — protocols for custom estimators
• ScipyGaussianKde — built-in method via scipy.stats.gaussian_kde (bandwidth: "scott", "silverman", or float)
• with_method(m) — returns an independent clone with a new method (shared sample, no copy)
• set_method(m) — replaces the estimator in place; cache and sampler reset automatically

Computation strategy

• EmpiricalComputationStrategy — extends DefaultComputationStrategy with:
  • Estimator-identity invalidation: detects _estimator swap via is-comparison on every query_method call; no explicit invalidate() needed
  • Vectorised PPF: CDF tabulation + PCHIP inversion, avoids per-quantile root-finding

Fixed

• DefaultUnuranSamplingStrategy.__deepcopy__ — returns a fresh uninitialised instance instead of trying to copy CFFI state; previously with_method crashed after the first sample() call