Define partype on types, mirroring eltype

[devmotion]

Motivation

In a downstream package I currently maintain an internal _partype that operates on distribution types, so that I can compute the parameter element type of a container of distributions from its eltype — without having to rely on the container being non-empty (i.e. without needing an instance). That internal version is necessarily incomplete: it reimplements per-distribution knowledge that already lives here and can't realistically cover every distribution.

The reason it's needed at all is that partype is currently only defined on instances: every distribution defines partype(d::Dist{T}) = T, with a Float64 fallback, so there's no way to ask partype(Normal{Float32}) for a type — it falls through to the default and silently returns the wrong answer.

This PR makes partype follow the same design as eltype: define it on the type, with the instance method provided for convenience. That makes the type-level query work directly and lets the downstream _partype go away.

Changes

• partype is now defined on the type, with partype(d) = partype(typeof(d)) forwarding for convenience, documented with a !!! note callout mirroring Base.eltype's docstring.
• All ~90 distribution methods migrated from partype(d::Dist{T}) to partype(::Type{<:Dist{T}}). Wrapper distributions (Censored, Truncated, AffineDistribution, ReshapedDistribution, OrderStatistic, JointOrderStatistics, MixtureModel, MvLogitNormal) recover the wrapped distribution from their type parameter, exactly as the matching eltype(::Type{...}) methods already do.
• The generic default changes from Float64 to Real: distribution parameters are <:Real and eltype(Real) === Real, so Real is the natural fallback (and zero/one work on it, unlike Any).
• Distributions that previously relied on the fallback get an explicit method. This fixes a latent bug where parametric distributions (Dirac, DiscreteNonParametric, Product, UnivariateGMM) reported Float64 instead of their actual parameter type. Parameterless distributions (Chernoff, Kolmogorov) return Union{} — the empty parameter promotion, which is the identity for promote_type and so composes correctly through wrappers; KSDist/KSOneSided return Int (their n), Soliton returns Float64.
• -(d::UnivariateDistribution) is changed from -one(partype(d)) * d to -one(promote_type(Int, partype(d))) * d so it stays well-typed when partype(d) === Union{} (the multiplier -1 is an Int, and promote_type(Int, Union{}) === Int).

Behavior changes

• partype(Dirac{Float32}) etc. now return the real parameter type (Float32) instead of Float64.
• partype(Kolmogorov()) / partype(Chernoff()) return Union{} (were Float64). One consequence: -Kolmogorov() now produces a LocationScale{Int,...} rather than silently a Float64-typed one.
• The generic fallback for an unknown distribution type is Real (was Float64).

Tests

• A general invariant wired into test/testutils.jl's test_params, so every distribution that runs the standard battery asserts:

  partype(d) === partype(typeof(d)) === mapreduce(recursive_partype, promote_type, params(d); init = Union{})

• partype tests live in each distribution's own test file (instance and type-based calls, instance forwarding, wrappers, the bug-fixes, and the Real/Union{} cases), covering the methods the standard battery does not exercise. To run all of them this:

  • enables univariate/discrete/bernoullilogit in runtests.jl (the file existed but was never included);
  • adds minimal test files for Hypergeometric, KSDist, and KSOneSided, which have no entry in the ref-data battery.

• The generic-mechanism regression tests live in test/univariate/continuous/normal.jl: the Real fallback for bare parametric UnionAlls (partype(Normal)) and abstract hierarchy nodes (partype(UnivariateDistribution)), plus the motivating partype(eltype(container)) for both concrete and abstract element types. A bare UnionAll's type parameters are only upper bounds, so the specific Type{<:Dist{T}} methods don't match and dispatch falls through to the Real default — exactly as eltype(Vector) === Any in Base. These lock that behavior in so a future subtyping change can't silently regress it.

• Every partype test is wrapped in @inferred, asserting the type-based design stays constant-foldable.

The full test suite passes (4,941,004 passing, 0 failures).

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 87.40%. Comparing base (6b5aa0d) to head (c52648f).

Additional details and impacted files

@@            Coverage Diff             @@
##           master    #2072      +/-   ##
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+ Coverage   86.74%   87.40%   +0.65%     
==========================================
  Files         149      149              
  Lines        8882     8891       +9     
==========================================
+ Hits         7705     7771      +66     
+ Misses       1177     1120      -57     

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