rs-stats

A comprehensive statistical library written in Rust, providing powerful tools for probability, distributions, and hypothesis testing.

rs-stats offers a broad range of statistical functionality implemented in pure Rust. It’s designed to be intuitive, efficient, and reliable for both simple and complex statistical analysis. The library aims to provide a comprehensive set of tools for data scientists, researchers, and developers working with statistical models.

Features

Probability Functions

• Error functions (erf, erfc)
• Cumulative distribution functions
• Probability density functions
• Z-scores
• Basic statistics (mean, variance, standard deviation, standard error)

Statistical Distributions

• Normal (Gaussian) distribution
• Binomial distribution
• Exponential distribution
• Poisson distribution
• Uniform distribution

Regression Analysis

• Linear Regression (fit, predict, confidence intervals)
• Multiple Linear Regression (multiple predictor variables)
• Model statistics (R², adjusted R², standard error)
• Model persistence (save/load models in JSON or binary format)

Hypothesis Testing

• ANOVA (Analysis of Variance)
• Chi-square tests (independence and goodness of fit)
• T-tests (one-sample, two-sample, paired)

Installation

Add rs-stats to your Cargo.toml:

[dependencies]
rs-stats = "1.2.1"

Or use cargo add:

cargo add rs-stats

Usage Examples

Basic Statistical Functions

use rs_stats::prob::{average, variance, population_std_dev, std_err};

fn main() {
let data = vec![1.0, 2.0, 3.0, 4.0, 5.0];

let mean = average(&data);
let var = variance(&data);
let std_dev = population_std_dev(&data);
let std_error = std_err(&data);

println!("Mean: {}", mean);
println!("Variance: {}", var);
println!("Standard Deviation: {}", std_dev);
println!("Standard Error: {}", std_error);
}

Working with Distributions

use rs_stats::distributions::normal_distribution::{normal_pdf, normal_cdf, normal_inverse_cdf};

fn main() {
// Standard normal distribution (mean=0, std_dev=1)
let x = 1.96;

// Probability density at x
let density = normal_pdf(x, 0.0, 1.0);
println!("PDF at {}: {}", x, density);

// Cumulative probability P(X ≤ x)
let cumulative = normal_cdf(x, 0.0, 1.0);
println!("CDF at {}: {}", x, cumulative);

// Inverse CDF (quantile function)
let p = 0.975;
let quantile = normal_inverse_cdf(p, 0.0, 1.0);
println!("{}th percentile: {}", p * 100.0, quantile);
}

Hypothesis Testing

use rs_stats::hypothesis_tests::t_test::{one_sample_t_test, two_sample_t_test};
use rs_stats::hypothesis_tests::chi_square_test::{chi_square_goodness_of_fit, chi_square_independence};
use rs_stats::hypothesis_tests::anova::one_way_anova;

fn main() {
// One-sample t-test
let sample = vec![5.1, 5.2, 4.9, 5.0, 5.3];
let result = one_sample_t_test(&sample, 5.0);
println!("One-sample t-test p-value: {}", result.p_value);

// Two-sample t-test
let sample1 = vec![5.1, 5.2, 4.9, 5.0, 5.3];
let sample2 = vec![4.8, 4.9, 5.0, 4.7, 4.9];
let result = two_sample_t_test(&sample1, &sample2);
println!("Two-sample t-test p-value: {}", result.p_value);

// ANOVA
let groups = vec![
vec![5.1, 5.2, 4.9, 5.0, 5.3],
vec![4.8, 4.9, 5.0, 4.7, 4.9],
vec![5.2, 5.3, 5.1, 5.4, 5.2],
];
let result = one_way_anova(&groups);
println!("ANOVA p-value: {}", result.p_value);

// Chi-square test of independence
let observed = vec![
vec![45, 55],
vec![60, 40],
];
let result = chi_square_independence(&observed);
println!("Chi-square independence test p-value: {}", result.p_value);
}

Regression Analysis

use rs_stats::regression::linear_regression::LinearRegression;
use rs_stats::regression::multiple_linear_regression::MultipleLinearRegression;

fn main() {
// Simple Linear Regression
let x = vec![1.0, 2.0, 3.0, 4.0, 5.0];
let y = vec![2.0, 4.0, 6.0, 8.0, 10.0];

let mut model = LinearRegression::new();
model.fit(&x, &y).unwrap();

println!("Slope: {}", model.slope);
println!("Intercept: {}", model.intercept);
println!("R-squared: {}", model.r_squared);

// Predict new values
let prediction = model.predict(6.0);
println!("Prediction for x=6: {}", prediction);

// Calculate confidence interval (95%)
if let Some((lower, upper)) = model.confidence_interval(6.0, 0.95) {
println!("95% confidence interval: ({}, {})", lower, upper);
}

// Multiple Linear Regression
let x_multi = vec![
vec![1.0, 2.0], // observation 1: x1.2.0, x2=2.0
vec![2.0, 1.0], // observation 2: x1=2.0, x2=1.0
vec![3.0, 3.0], // observation 3: x1=3.0, x2=3.0
vec![4.0, 2.0], // observation 4: x1=4.0, x2=2.0
];
let y_multi = vec![9.0, 8.0, 16.0, 15.0];

let mut multi_model = MultipleLinearRegression::new();
multi_model.fit(&x_multi, &y_multi).unwrap();

println!("Coefficients: {:?}", multi_model.coefficients);
println!("R-squared: {}", multi_model.r_squared);
println!("Adjusted R-squared: {}", multi_model.adjusted_r_squared);

// Predict with multiple variables
let new_observation = vec![5.0, 4.0];
let prediction = multi_model.predict(&new_observation);
println!("Prediction for new observation: {}", prediction);

// Save model to file
multi_model.save("model.json").unwrap();

// Load model from file
let loaded_model = MultipleLinearRegression::load("model.json").unwrap();
}

Decision Trees

use rs_stats::regression::decision_tree::{DecisionTree, TreeType, SplitCriterion};

// Example 1: Regression Tree for Patient Recovery Time Prediction
let mut recovery_time_tree = DecisionTree::<f64, f64>::new(
TreeType::Regression,
SplitCriterion::Mse,
5,   // max_depth
2,   // min_samples_split
1    // min_samples_leaf
);

// Training data: [age, treatment_intensity, bmi, comorbidity_score, initial_severity]
let patient_features = vec![
vec![45.0, 3.0, 28.5, 2.0, 7.0],  // Patient 1: 45 years, treatment intensity 3, BMI 28.5, etc.
vec![62.0, 4.0, 31.2, 3.0, 8.0],  // Patient 2
vec![38.0, 2.0, 24.3, 1.0, 5.0],  // Patient 3
// ... more patients
];
let recovery_days = vec![14.0, 28.0, 10.0];  // Recovery time in days

// Train the model to predict recovery time
recovery_time_tree.fit(&patient_features, &recovery_days);

// Make predictions for a new patient
let new_patient = vec![
vec![55.0, 3.0, 27.0, 2.0, 6.0],  // New patient characteristics
];
let predicted_recovery_days = recovery_time_tree.predict(&new_patient);

// Example 2: Classification Tree for Diabetes Risk Assessment
let mut diabetes_risk_tree = DecisionTree::<u8, f64>::new(
TreeType::Classification,
SplitCriterion::Gini,
4,   // max_depth
2,   // min_samples_split
1    // min_samples_leaf
);

// Training data: [glucose_level, bmi, blood_pressure, age, family_history]
let medical_features = vec![
vec![85.0, 22.0, 120.0, 35.0, 0.0],  // Patient 1: glucose 85 mg/dL, BMI 22, BP 120, etc.
vec![140.0, 31.0, 145.0, 52.0, 1.0],  // Patient 2
vec![165.0, 34.0, 155.0, 48.0, 1.0],  // Patient 3
// ... more patients
];
let diabetes_status = vec![0, 1, 1];  // 0: No diabetes, 1: Diabetes

// Train the classifier
diabetes_risk_tree.fit(&medical_features, &diabetes_status);

// Print tree structure and summary
println!("Tree Structure:\n{}", diabetes_risk_tree.tree_structure());
println!("Tree Summary:\n{}", diabetes_risk_tree.summary());

// Feature importance - which medical measurements are most predictive
let importance = diabetes_risk_tree.feature_importances();
println!("Feature Importance: {:?}", importance);

The Decision Tree implementation supports:

• Both regression and classification tasks
• Multiple split criteria (MSE, MAE for regression; Gini, Entropy for classification)
• Generic types with appropriate trait bounds
• Parallel processing for optimal performance
• Tree visualization and interpretation tools
• Feature importance calculation

Documentation

For detailed API documentation, run:

cargo doc --open

Testing

The library includes a comprehensive test suite. Run the tests with:

cargo test

Contributing

Contributions are welcome! Here’s how you can contribute:

1. Fork the repository
2. Create a feature branch: git checkout -b feature/my-new-feature
3. Commit your changes: git commit -am 'Add some feature'
4. Push to the branch: git push origin feature/my-new-feature
5. Submit a pull request

Before submitting your PR, please make sure:

• All tests pass
• Code follows the project’s style and conventions
• New features include appropriate documentation and tests

License

This project is licensed under the MIT License - see the LICENSE file for details.

Acknowledgments

• The Rust community for their excellent documentation and support
• Contributors to the project
• Various statistical references and research papers that informed the implementations