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 = "1.2.0"

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