StatMath

StatMath - Comprehensive Statistical Functions Library

This is the main autoload singleton that provides access to all statistical functions and mathematical utilities. All core functionality is organized into specialized modules that can be accessed through this central interface.

Usage Examples:

# Generate random numbers from distributions
var normal_sample = StatMath.Distributions.randf_normal(0.0, 1.0)
var poisson_sample = StatMath.Distributions.randi_poisson(3.5)

# Calculate statistical measures
var data = [1.0, 2.0, 3.0, 4.0, 5.0]
var mean = StatMath.BasicStats.mean(data)
var variance = StatMath.BasicStats.variance(data)

# Use distribution functions
var cdf_value = StatMath.CdfFunctions.normal_cdf(1.96, 0.0, 1.0)
var quantile = StatMath.PpfFunctions.normal_ppf(0.975, 0.0, 1.0)

# Advanced sampling
var samples = StatMath.SamplingGen.generate_samples(100, 2, StatMath.SamplingGen.SamplingMethod.SOBOL)

Module Organization:

BasicStats - Descriptive statistics (mean, variance, quantiles, etc.)
Distributions - Random number generation from various distributions
CdfFunctions - Cumulative distribution functions
PpfFunctions - Inverse CDF/quantile functions
PmfPdfFunctions - Probability mass/density functions
ErrorFunctions - Error functions and special mathematical functions
HelperFunctions - Core mathematical utilities
SamplingGen - Advanced sampling and quasi-random sequences

Usage

# StatMath is the main singleton - access modules through it
var result = StatMath.ModuleName.function_name(parameters)

# Or access constants directly
var epsilon = StatMath.EPSILON

Constants

GODOT_STAT_MATH_SEED_VARIABLE_NAME: Value: StringName = &"godot_stat_math_seed"

_default_seed: Value: int = 0

PRIMES: Value: Array[int] = [

INT_MAX_REPRESENTING_INF: Value: = 2147483647

INT64_MAX_VAL: Value: int = 9223372036854775807

FLOAT_EPSILON: Value: float = 2.220446049250313e-16

MAX_ITERATIONS: Value: int = 200

EPSILON: Value: float = 1.0e-9

FLOAT_TOLERANCE: Value: float = 1.0e-7

HIGH_PRECISION_TOLERANCE: Value: float = 1.0e-9

ERF_APPROX_TOLERANCE: Value: float = 1.0e-5

NUMERICAL_DIFFERENTIATION_H: Value: float = 1.0e-6

SAMPLE_MEAN_TOLERANCE: Value: float = 1.0e-6

SAMPLING_DETERMINISM_TOLERANCE: Value: float = 1.0e-7

INVERSE_FUNCTION_TOLERANCE: Value: float = 2.0e-6

NUMERICAL_TOLERANCE: Value: float = 1.0e-5

CDF_PPF_CONSISTENCY_TOLERANCE: Value: float = 1.0e-5

DERIVATIVE_TOLERANCE: Value: float = 1.0e-3

PROBABILITY_TOLERANCE: Value: float = 1.0e-6

SPECIAL_VALUES_TOLERANCE: Value: float = 2.0e-6

BOUNDARY_TOLERANCE: Value: float = 1.0e-10

ASYMPTOTIC_TOLERANCE: Value: float = 1.0e-2

INTERPOLATION_TOLERANCE: Value: float = 1.0e-4

NUMERICAL_INTEGRATION_TOLERANCE: Value: float = 5.0e-3

SYMMETRY_TOLERANCE: Value: float = 1.0e-4

ERF_INV_TOLERANCE: Value: float = 2.0e-2

STATISTICAL_TEST_STD_DEV_MULTIPLIER: Value: float = 4.0

DEFAULT_TOLERANCE_FACTOR: Value: float = 1.0

SAMPLING_TOLERANCE: Value: float = 1.0e-6

INVERSE_CONSISTENCY_TOLERANCE: Value: float = 1.0e-5

STABILITY_TOLERANCE: Value: float = 1.0e-6

STRESS_TEST_BOUNDARY: Value: float = 1.0e-17

STRESS_TEST_SMALL_VALUE: Value: float = 1.0e-3

INTERFACE_TOLERANCE: Value: float = 1.0e-7

DETERMINISM_TOLERANCE: Value: float = 1.0e-7

HYPERGEOMETRIC_TOLERANCE: Value: float = 0.15

NEGATIVE_BINOMIAL_TOLERANCE: Value: float = 0.2

HIGH_DISTRIBUTION_TOLERANCE: Value: float = 0.5

BETA_TOLERANCE: Value: float = 0.1

LANCZOS_G: Value: float = 7.5

LANCZOS_P: Value: Array[float] = [

A1_ERR: Value: float = 0.254829592

A2_ERR: Value: float = -0.284496736

A3_ERR: Value: float = 1.421413741

A4_ERR: Value: float = -1.453152027

A5_ERR: Value: float = 1.061405429

P_ERR: Value: float = 0.3275911

BasicStats: Value: preload("res://addons/godot-stat-math/core/basic_stats.gd")

Distributions: Value: preload("res://addons/godot-stat-math/core/distributions.gd")

CdfFunctions: Value: preload("res://addons/godot-stat-math/core/cdf_functions.gd")

PmfPdfFunctions: Value: preload("res://addons/godot-stat-math/core/pmf_pdf_functions.gd")

PpfFunctions: Value: preload("res://addons/godot-stat-math/core/ppf_functions.gd")

ErrorFunctions: Value: preload("res://addons/godot-stat-math/core/error_functions.gd")

HelperFunctions: Value: preload("res://addons/godot-stat-math/core/helper_functions.gd")

SamplingGen: Value: preload("res://addons/godot-stat-math/core/sampling_gen.gd")

Functions

_ready() → void:

Initializes the StatMath addon and sets up the random number generator.

Automatically called when the addon is loaded as an autoload singleton. Reads the global seed configuration and initializes the RNG system.

_create_and_seed_rng(seed_val: int) → void:

Creates and seeds the internal RandomNumberGenerator instance.

If seed_val is 0, Godot will automatically choose a random seed. The actual seed used can be read from _rng.seed after initialization.

_initialize_rng() → void:

Initializes the RNG system using global project settings.

Checks for the project setting godot_stat_math_seed to determine the seed value. Creates the setting with default value if it doesn’t exist.

get_rng() → RandomNumberGenerator:

Returns the addon’s RandomNumberGenerator instance.

This RNG is used by all statistical functions that require randomness. Provides consistent seeding and reproducible results across the addon.

Mathematical Note: All statistical sampling uses this centralized RNG for reproducibility

set_global_seed(new_seed: int) → void:

Changes the global seed and recreates the RandomNumberGenerator.

This affects all subsequent random number generation throughout the addon. Useful for creating reproducible statistical simulations and tests.

Mathematical Note: Changing seed allows reproducible statistical experiments