Add Liouville copulas

[lrnv]

Closes #405

This adds a generator-first Liouville copula implementation with arbitrary positive Dirichlet parameters and generic radial distributions derived through Williamson inversion.

It includes sampling, density and CDF evaluation, marginalization, conditioning, Rosenblatt transforms, support for real Williamson orders, documentation, and targeted tests. Integer conditioning orders retain the existing tilted-generator path; fractional orders use the conditional radial representation.

The generic test bestiary covers preserved Williamson radials and ordinary Clayton generators with both integer and non-integer alpha parameters. The CI should also help identify the cost of the fractional-order numerical paths.

[github-actions]

🟢 Tachometer — no performance regressions detected (1 improvement 🟢)

25 benchmarks compared · 579cef3 → d9abb7e · Julia 1.12.7 · 5% tolerance · 3× runs

	Benchmark	Time	Memory
🟢	sampling/clayton_d5	7.03 ms → 2.3 ms (−67%)	547 KiB → 391 KiB (−29%)

Full results (25 benchmarks)

	Benchmark	Time	Memory
⚪️	cdf/bb1_d2	1.55 ms → 1.56 ms (+1%)	—
⚪️	cdf/galambos_d2	1.33 ms → 1.33 ms (+0%)	—
⚪️	conditioning/cdf_bb1_d2	335 µs → 336 µs (+0%)	—
⚪️	conditioning/construct_bb1_d2_1000	633 µs → 638 µs (+1%)	—
⚪️	conditioning/inverse_rosenblatt_gaussian_d5	263 µs → 264 µs (+0%)	—
⚪️	conditioning/quantile_galambos_d2	11.4 ms → 11.4 ms (−0%)	—
⚪️	conditioning/rosenblatt_gaussian_d5	297 µs → 298 µs (+0%)	—
⚪️	data/beta_logpdf	10.3 ms → 10.2 ms (−1%)	—
⚪️	data/checkerboard_cdf	56.1 ms → 53.6 ms (−4%)	—
⚪️	data/empirical_cdf	15.2 ms → 15.2 ms (−0%)	—
⚪️	data/pseudos_5x10000	1.97 ms → 1.98 ms (+1%)	—
⚪️	density/bb1_d2	1.86 ms → 1.86 ms (+0%)	—
⚪️	density/galambos_d2	2.53 ms → 2.53 ms (+0%)	—
⚪️	density/gaussian_d10	8.53 ms → 8.59 ms (+1%)	—
⚪️	density/gumbel_d5	8.97 ms → 9.01 ms (+0%)	—
⚪️	density/nested_d6	10.4 ms → 10.3 ms (−0%)	—
⚪️	fitting/gaussian_mle	54.7 µs → 55.1 µs (+1%)	—
⚪️	fitting/gumbel_itau	143 µs → 143 µs (−0%)	—
⚪️	fitting/sklar_ifm	54.4 ms → 53.6 ms (−2%)	38.3 MiB → 37.9 MiB (−1%)
⚪️	sampling/archimax_d2	16.7 ms → 16.7 ms (+0%)	—
🟢	sampling/clayton_d5	7.03 ms → 2.3 ms (−67%)	547 KiB → 391 KiB (−29%)
⚪️	sampling/galambos_d2	82.2 ms → 82.2 ms (−0%)	—
⚪️	sampling/gaussian_d10	1.73 ms → 1.73 ms (−0%)	—
⚪️	sampling/nested_d6	121 ms → 120 ms (−1%)	—
⚪️	sampling/student_d2	4.4 ms → 4.4 ms (+0%)	—

_{baseline 579cef3 · target d9abb7e · Julia 1.12.7 · ARM Neoverse-N2 · min estimator · tol 5%/5% · floor 1 µs · 3× runs · run · Tachometer.jl}

[codecov]

Codecov Report

❌ Patch coverage is 94.81865% with 20 lines in your changes missing coverage. Please review.
✅ Project coverage is 83.50%. Comparing base (579cef3) to head (d9abb7e).
⚠️ Report is 1 commits behind head on main.

Files with missing lines	Patch %	Lines
src/Generator/ClaytonGenerator.jl	78.94%	8 Missing ⚠️
...riateDistribution/Radials/WilliamsonFromFrailty.jl	92.94%	6 Missing ⚠️
src/LiouvilleCopula.jl	98.00%	4 Missing ⚠️
src/Generator.jl	97.87%	1 Missing ⚠️
...tribution/Radials/ClaytonWilliamsonDistribution.jl	91.66%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main     #416      +/-   ##
==========================================
+ Coverage   82.47%   83.50%   +1.03%     
==========================================
  Files          87       88       +1     
  Lines        6328     6640     +312     
==========================================
+ Hits         5219     5545     +326     
+ Misses       1109     1095      -14     

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