feat(kde): kernel functions with statistical properties and LOESS support

[thisisamirv]

Add kernel functions with statistical properties and LOESS support

This PR prepares the foundation for KDE and LOESS implementations.

Summary

Major enhancement to the kernel module adding:

1. Kernel density estimation (KDE) constants to consts.rs
2. Complete rewrite of kernel.rs with AMISE efficiency metrics, dual evaluation modes, and LOESS integration
3. Compile-time validation of statistical properties

Changes to consts.rs

• Kernel variance (μ₂): ∫ u² K(u) du for 9 kernels
• Kernel roughness (R(K)): ∫ K(u)² du for 9 kernels
• Module docs explaining kernel properties and bandwidth conversion
• References to Silverman (1986) Table 3.1 and Wand & Jones (1995)
• Added missing SQRT_PI constant

Changes to kernel.rs

1. Statistical Correctness

• Dual evaluation modes:
  • evaluate(): Normalized for KDE (integrates to 1)
  • evaluate_weight(): Unnormalized for LOESS (local regression weights)
• AMISE properties: Efficiency, variance, roughness, bandwidth factors from Silverman (1986)
• Compile-time validation: Ensures efficiency calculations match theoretical values

2. New Kernels & Renaming

• Renamed Quartic → Bisquare (it's a more standard name)
• Added Cosine kernel (high efficiency ≈ 0.9995)
• Added Logistic kernel (heavy-tailed unbounded)
• Added Sigmoid kernel (hyperbolic secant)
• Fixed Sigmoid formula: was exp(πx), now correctly exp(x)

3. Enhanced API

• KernelType enum: Runtime kernel selection for LOESS and other applications
• CustomKernel: User-defined kernels with metadata
• Batch operations: evaluate_batch(), compute_distance_weights()
• Utilities: robust_reweights(), normalize_weights()
• Recommendations: recommended_for_kde(), recommended_for_loess(), most_efficient()

4. Boundary Behavior Fix

• Changed boundary handling from |x| <= 1 to |x| >= 1 for consistency
• Support now returns open interval (-1, 1) as mathematically correct
• All bounded kernels return 0 at exactly x = ±1

5. Documentation & Testing

• Comprehensive table: Formula, support, efficiency, R(K), μ₂(K) for all kernels
• Compile-time tests: Verify efficiency matches Silverman (1986) exact values
• Many runtime tests: Integration, symmetry, monotonicity, normalization, edge cases

Breaking Changes

1. Quartic → Bisquare: Renamed for statistical consistency
2. Boundary behavior: |x| = 1 now returns 0 (was non-zero)
3. Sigmoid formula: Fixed to match hyperbolic secant definition
4. Tricube normalization: Now (70/81)(1-|x|³)³ (was unnormalized)

Fixed

• Fix unused import warnings for distribution (removed unused import crate::distribution::internal::testing_boiler).
• Fix Geometric::inverse_cdf platform-dependent behavior on Windows:

Problem

The test_inverse_cdf test was failing on Windows with:

• Expected: 1
• Got: 2 for inverse_cdf(0.0)

Root Cause

Floating-point precision differences across platforms caused inverse_cdf(0.0) to compute inconsistent results when using the formula ceil(log(1-p) / log(1-self.p)).

Solution

Added an explicit implementation of inverse_cdf for the Geometric distribution that handles edge cases consistently:

• Returns min() (1) when input probability p <= 0.0
• Returns 1 when distribution parameter self.p == 1.0
• Returns max() (u64::MAX) when input probability p >= 1.0
• Uses the mathematical formula for other cases

This ensures consistent behavior across all platforms (macOS, Linux, Windows).

[codecov]

Codecov Report

❌ Patch coverage is 95.62044% with 54 lines in your changes missing coverage. Please review.
✅ Project coverage is 94.73%. Comparing base (5da3470) to head (8325b1a).
⚠️ Report is 6 commits behind head on master.

Files with missing lines	Patch %	Lines
src/function/kernel.rs	95.65%	53 Missing ⚠️
src/distribution/geometric.rs	92.30%	1 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #360      +/-   ##
==========================================
- Coverage   94.99%   94.73%   -0.27%     
==========================================
  Files          61       59       -2     
  Lines       13615    14004     +389     
==========================================
+ Hits        12934    13266     +332     
- Misses        681      738      +57     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[YeungOnion]

Hey, would you be willing to break this one out across a few PRs?

One partition could be,

• fixes and changes to kernel functions, additions for consts and compile time testing
• kerneltype enum and custom kernel (happy to discuss this, but we've not implemented a lot in the way of dynamic dispatch)
• fixing geometric inverse cdf is worked on in feat: add specialised inverse cdf implementation for geometric distribution #343 (I should move that forward and make additional tests into a separate issue)
• fix for macro imports and use - I don't know why this lint appears in this context.