Godot Stat Math

Getting Started

  • Installation
    • Prerequisites
    • Installation Methods
      • Asset Library (Recommended)
      • Manual Installation
      • Git Submodule (For Developers)
    • Verification
    • Configuration
      • Optional: Set Global Seed
    • Troubleshooting
      • Plugin Not Appearing
      • StatMath Not Available
      • Getting Help
  • Quick Start Guide
    • Basic Usage
    • Core Modules Overview
    • Common Use Cases
      • Analyzing Player Data
      • Procedural Content Generation
      • Random Events with Probabilities
      • Advanced Sampling for Level Generation
    • Working with Distributions
      • Understanding the Flow
      • Example: Balancing a Random Event
    • Data Cleaning and Preprocessing
    • Reproducible Results
    • Next Steps

Core Modules

  • StatMath
    • Usage
    • Constants
      • GODOT_STAT_MATH_SEED_VARIABLE_NAME
      • _default_seed
      • PRIMES
      • INT_MAX_REPRESENTING_INF
      • INT64_MAX_VAL
      • FLOAT_EPSILON
      • MAX_ITERATIONS
      • EPSILON
      • FLOAT_TOLERANCE
      • HIGH_PRECISION_TOLERANCE
      • ERF_APPROX_TOLERANCE
      • NUMERICAL_DIFFERENTIATION_H
      • SAMPLE_MEAN_TOLERANCE
      • SAMPLING_DETERMINISM_TOLERANCE
      • INVERSE_FUNCTION_TOLERANCE
      • NUMERICAL_TOLERANCE
      • CDF_PPF_CONSISTENCY_TOLERANCE
      • DERIVATIVE_TOLERANCE
      • PROBABILITY_TOLERANCE
      • SPECIAL_VALUES_TOLERANCE
      • BOUNDARY_TOLERANCE
      • ASYMPTOTIC_TOLERANCE
      • INTERPOLATION_TOLERANCE
      • NUMERICAL_INTEGRATION_TOLERANCE
      • SYMMETRY_TOLERANCE
      • ERF_INV_TOLERANCE
      • STATISTICAL_TEST_STD_DEV_MULTIPLIER
      • DEFAULT_TOLERANCE_FACTOR
      • SAMPLING_TOLERANCE
      • INVERSE_CONSISTENCY_TOLERANCE
      • STABILITY_TOLERANCE
      • STRESS_TEST_BOUNDARY
      • STRESS_TEST_SMALL_VALUE
      • INTERFACE_TOLERANCE
      • DETERMINISM_TOLERANCE
      • HYPERGEOMETRIC_TOLERANCE
      • NEGATIVE_BINOMIAL_TOLERANCE
      • HIGH_DISTRIBUTION_TOLERANCE
      • BETA_TOLERANCE
      • LANCZOS_G
      • LANCZOS_P
      • A1_ERR
      • A2_ERR
      • A3_ERR
      • A4_ERR
      • A5_ERR
      • P_ERR
      • BasicStats
      • Distributions
      • CdfFunctions
      • PmfPdfFunctions
      • PpfFunctions
      • ErrorFunctions
      • HelperFunctions
      • SamplingGen
    • Functions
      • _ready()
      • _create_and_seed_rng()
      • _initialize_rng()
      • get_rng()
      • set_global_seed()
  • StatMath.BasicStats
    • Usage
    • Functions
      • mean()
      • median()
      • variance()
      • standard_deviation()
      • sample_variance()
      • sample_standard_deviation()
      • median_absolute_deviation()
      • range_spread()
      • minimum()
      • maximum()
      • percentile()
      • summary_statistics()
  • StatMath.Distributions
    • Usage
    • Functions
      • randi_bernoulli()
      • randi_binomial()
      • randi_geometric()
      • randi_poisson()
      • randi_uniform()
      • randi_pseudo()
      • randi_seige()
      • randf_uniform()
      • randf_exponential()
      • randf_erlang()
      • randf_gamma()
      • randf_beta()
      • randf_gaussian()
      • randf_normal()
      • randf_lognormal()
      • randf_cauchy()
      • randf_triangular()
      • randf_pareto()
      • randf_weibull()
      • randv_histogram()
  • StatMath.CdfFunctions
    • Usage
    • Functions
      • uniform_cdf()
      • normal_cdf()
      • exponential_cdf()
      • beta_cdf()
      • gamma_cdf()
      • chi_square_cdf()
      • f_cdf()
      • t_cdf()
      • binomial_cdf()
      • poisson_cdf()
      • geometric_cdf()
      • negative_binomial_cdf()
      • pareto_cdf()
      • weibull_cdf()
      • cauchy_cdf()
      • lognormal_cdf()
  • StatMath.PpfFunctions
    • Usage
    • Constants
      • ACKLAM_COEFFICIENTS
    • Functions
      • uniform_ppf()
      • normal_ppf()
      • exponential_ppf()
      • beta_ppf()
      • _beta_2_2_ppf_fast()
      • gamma_ppf()
      • chi_square_ppf()
      • f_ppf()
      • t_ppf()
      • binomial_ppf()
      • poisson_ppf()
      • geometric_ppf()
      • negative_binomial_ppf()
      • bernoulli_ppf()
      • discrete_histogram_ppf()
      • pareto_ppf()
      • weibull_ppf()
  • StatMath.PmfPdfFunctions
    • Usage
    • Functions
      • binomial_pmf()
      • poisson_pmf()
      • negative_binomial_pmf()
      • geometric_pmf()
      • normal_pdf()
      • exponential_pdf()
      • uniform_pdf()
      • gamma_pdf()
      • beta_pdf()
      • weibull_pdf()
      • lognormal_pdf()
      • chi_squared_pdf()
      • t_pdf()
      • f_pdf()
      • cauchy_pdf()
      • pareto_pdf()
  • StatMath.ErrorFunctions
    • Usage
    • Functions
      • erf()
      • erfc()
      • erf_inv()
      • erfc_inv()
      • log_gamma()
      • gamma()
  • StatMath.HelperFunctions
    • Usage
    • Functions
      • binomial_coefficient()
      • log_factorial()
      • log_binomial_coef()
      • gamma_function()
      • log_gamma()
      • beta_function()
      • log_beta_function_direct()
      • incomplete_beta()
      • lower_incomplete_gamma_regularized()
      • _gamma_series_expansion()
      • _gamma_continued_fraction()
      • sanitize_numeric_array()
      • convert_to_float_array()
      • validate_indices()
      • validate_unique_indices()
      • get_cdf_value()
      • get_ppf_value()
      • string_to_distribution_enum()
  • StatMath.SamplingGen
    • Usage
    • Constants
      • _SOBOL_DATA
      • _PRIME_DATA
      • _SOBOL_BITS
      • _SOBOL_MAX_VAL_FLOAT
      • MAX_POOLED_DECKS_PER_SIZE
    • Functions
      • _init()
      • _get_pooled_deck()
      • _return_pooled_deck()
      • _ensure_sobol_vectors_initialized()
      • _generate_direction_vectors_for_dimension()
      • _generate_dimension_samples_worker()
      • _batch_shuffle_worker()
      • _create_unshuffled_deck()
      • _coordinated_shuffle_with_samples()
      • _coordinated_shuffle_worker()
      • _with_replacement_draw()
      • _fisher_yates_draw()
      • _reservoir_draw()
      • _selection_tracking_draw()
      • _get_nth_prime()
      • _get_sobol_1d_integers()
      • _generate_sobol_1d()
      • _generate_halton_1d()
      • _generate_latin_hypercube_1d()
      • _fast_random_batch_shuffles()
      • _fast_random_shuffle()

Tests

  • Unit Testing
    • Test Coverage
    • Test Results Overview
    • Understanding Test Status
  • Performance Testing
    • Test Methodology
    • Understanding the Results
  • Testing Standards
    • Overview
    • 1. Standards & Philosophy
      • Core Principles
      • 1. The Dual-Pillar Testing Strategy
      • 2. Test Organization and Structure
      • Data-Driven Standards
      • Required Table Data Structure
      • Scipy Version Control
      • Acceptable Hardcoded Values
      • Exception: Simple, Illustrative Test Data
      • Data Generation Requirements
      • Tolerance Constants Usage
      • Tolerance Decision Tree
      • Standard Tolerances
      • Specialized Tolerances
      • Tolerance Selection Guidelines
    • 2. Implementation & Organization
      • Folder Structure
      • Implementation Guidelines
      • File Naming Convention
      • Test Implementation Patterns
      • Types of Testing Approaches
        • 1. Data-Driven Testing (Primary Approach)
        • 2. Example-Based Testing (Simple Cases Only)
        • 3. Property-Based Testing (Future Enhancement)
      • Standard Test Function Pattern
      • Parametrized Test Pattern
      • Error Testing Pattern
      • File Organization Standards
      • Data Table Standards
        • 1. Generated by generate_test_data.py:
        • 2. Downloaded from authoritative sources
      • Documentation Standards
      • Test Documentation
      • Code Comments
      • Scipy Call Documentation
      • Error Handling Standards
      • Error Testing Requirements
      • Error Message Format
    • 3. Infrastructure & Process
      • CI/CD Integration and Platform Consistency
      • Development Workflow
        • Core Branches
        • PR to develop (verify-develop.yaml)
        • Merge PR into develop (build-develop.yaml)
        • PR to release (verify-release.yaml)
        • Merge PR into release (build-release.yaml)
        • Key Benefits:
        • Other Workflows:
      • Testing Workflow
      • 1. Data Generation Process
      • 2. Test Implementation Process
      • 3. Quality Assurance Process
    • 4. Performance Testing
      • Performance Test Infrastructure
      • Baseline Generation:
      • Threshold Determination:
      • Known Regression Handling:
      • Baseline Regeneration:
      • Performance Considerations
      • Test Execution Efficiency
      • Memory Management
      • Test Data Governance Process
      • Minimal Governance Philosophy
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