Add Property-Based Testing with Random Parameter Generation

[edzillion]

Overview

Our current test suite has excellent mathematical property testing but lacks true property-based testing with random parameter generation. We should complement our existing example-based tests with property-based tests that use randomly generated inputs to catch edge cases.

Current State: Strong Foundation ✅

• Excellent test organization with dedicated mathematical_property_test.gd files
• Testing the RIGHT mathematical properties (monotonicity, round-trip consistency, boundary conditions)
• Great coverage of numerical stability and edge cases
• Comprehensive scipy validation with data-driven approach

Missing: True Property-Based Testing ❌

Our tests currently use fixed test cases rather than generated random inputs:

Current Pattern (Example-Based):

func test_pareto_cdf_monotonicity() -> void:
    # Fixed test points
    var x1: float = 2.5
    var x2: float = 3.0
    var x3: float = 4.0
    # Test specific cases...

Needed Pattern (Property-Based):

func test_pareto_cdf_monotonicity_property() -> void:
    var rng = RandomNumberGenerator.new()
    rng.seed = 12345  # Deterministic for CI
    
    # Generate many random test cases
    for i in range(100):
        var scale = rng.randf_range(0.1, 10.0)
        var shape = rng.randf_range(0.5, 5.0)
        var x1 = rng.randf_range(scale, scale * 10.0)
        var x2 = x1 + rng.randf_range(0.1, 5.0)
        
        # Property: CDF should be monotonic
        var cdf1 = StatMath.CdfFunctions.pareto_cdf(x1, scale, shape)
        var cdf2 = StatMath.CdfFunctions.pareto_cdf(x2, scale, shape)
        assert_float(cdf1).is_less_equal(cdf2)

Proposed Improvements

1. CDF Functions

• Random parameter generation for range validation (CDF ∈ [0,1])
• Random monotonicity testing across parameter spaces
• Random boundary condition validation

2. Basic Statistics

• Generated data property testing (variance ≥ 0)
• Random data transformation properties
• Scale/translation invariance with random data

3. PPF Functions

• Enhanced round-trip consistency with random parameters
• Random monotonicity validation
• Random boundary behavior testing

Implementation Strategy

• Keep existing tests: Current scipy validation and example-based tests are valuable
• Add complementary property-based tests: New test functions with _property suffix
• Use deterministic seeds: Ensure CI reproducibility
• Reasonable test counts: Balance coverage vs execution time (50-200 iterations per property)

Success Criteria

• All CDF functions have property-based range validation
• All statistical functions have property-based invariant testing
• All PPF functions have enhanced round-trip property testing
• Maintain existing test pass rates
• No significant CI execution time increase

Priority

Medium - This enhancement will improve test coverage and catch edge cases, but existing test suite already provides strong validation.