Rename `mean` constructor parameter to `mu` on BetaProportion and NegativeBinomial2

[tillahoffmann]

Problem

Two distributions take a constructor parameter literally named mean, which collides with the .mean statistic property every distribution exposes:

• BetaProportion(mean, concentration) — continuous.py:3408; "mean" in arg_constraints (open_interval(0, 1)).
• NegativeBinomial2(mean, concentration) — conjugate.py:533; "mean" in arg_constraints (positive). The name also propagates to the ZeroInflatedNegativeBinomial2 and HurdleNegativeBinomial2 factory functions.

Neither class stores self.mean. The constructor immediately reparameterizes the argument (BetaProportion → concentration1/concentration0; NegativeBinomial2 → rate = concentration / mean) and stores those instead. So arg_constraints["mean"] validation reads getattr(self, "mean"), which resolves to the inherited .mean statistic property (Beta.mean / GammaPoisson.mean). That happens to equal the input only by the reparameterization algebra:

• BetaProportion: μφ / (μφ + (1−μ)φ) = μ
• NegativeBinomial2: α / (α/μ) = μ

Why it matters

Validation of the mean parameter is silently piggybacking on the .mean statistic, relying on an algebraic coincidence rather than checking the actual input. This is fragile: when Beta.mean was narrowed to return a jax.Array (jnp.asarray(...)), the property became a tracer under jax.jit, so Distribution.validate_args(strict=False) skipped value validation and test_distribution_constraints' under-jit assertion broke for BetaProportion. (Worked around in the array-output PR by relaxing that test assertion.)

Proposed fix

Rename the constructor parameter mean → mu on both distributions (and the two NB2 factory functions), updating arg_constraints, reparametrized_params, docstrings, and any examples/tests. mu matches both distributions' references (Ferrari & Cribari-Neto 2004 for BetaProportion; the NB2 docstring already writes μ) and removes the attribute-name collision. The .mean property continues to compute the statistic; there is no longer a parameter shadowing it.

loc was considered and rejected: these parameters are the mean of a bounded/count distribution, not an additive location shift, so loc would misrepresent the parameterization.

Compatibility

This is a breaking public API change (both classes are exported and documented). It needs a deprecation path — accept mu as the new name, keep mean working with a DeprecationWarning for at least one release.