Crate normality 

normality

A Rust crate for assessing the normality of a data sample. It provides several common statistical tests to determine if a set of data is likely drawn from a normal distribution.

All test implementations are generic and can work with f32 or f64 data types. The implementations are ported from well-established algorithms found in popular R packages.

Implemented Tests

• Shapiro-Wilk Test: One of the most powerful tests for normality.
• Lilliefors (Kolmogorov-Smirnov) Test: A modification of the K-S test for when population mean and variance are unknown.
• Anderson-Darling Test: Gives more weight to the tails of the distribution.
• Jarque-Bera Test: Tests whether the sample skewness and kurtosis match a normal distribution.
• Pearson Chi-squared Test: A goodness-of-fit test that compares observed and expected frequencies.
• Cramer-von Mises Test: An alternative EDF goodness-of-fit test.
• D’Agostino’s K-squared Test: Tests for normality based on sample skewness.

Installation

Either run cargo add normality or add the crate to your Cargo.toml:

[dependencies]
normality = "1.0.0"

Example Usage

use normality::{shapiro_wilk, Error};

fn main() -> Result<(), Error> {
    // Sample data that is likely from a normal distribution
    let data = vec![-1.1, -0.8, -0.5, -0.2, 0.0, 0.2, 0.5, 0.8, 1.1, 1.3];

    // Perform the Shapiro-Wilk test
    let result = shapiro_wilk(&data)?;

    println!("Shapiro-Wilk Test Results:");
    println!("  W-statistic: {:.4}", result.statistic);
    println!("  p-value: {:.4}", result.p_value);

    // Interpretation: A high p-value (e.g., > 0.05) suggests that the data
    // does not significantly deviate from a normal distribution.
    if result.p_value > 0.05 {
        println!("Conclusion: The sample is likely from a normal distribution.");
    } else {
        println!("Conclusion: The sample is not likely from a normal distribution.");
    }

    Ok(())
}

Accuracy

The accuracy of the implemented tests has been verified against their R equivalents. Running the integration tests for this crate requires a local installation of R and for the Rscript executable to be available in the system’s PATH.

License

This project is licensed under the MIT License.

Structs

Computation

A generic data structure to hold the results of a normality test.

Enums

Error

Represents errors that can occur during a normality test computation.

Traits

Float

A convenience trait combining bounds frequently used for floating-point computations.

Functions

anderson_darling

Performs the Anderson-Darling test for normality.

dagostino_k_squared

Performs D’Agostino’s K-squared test for skewness to assess normality.

jarque_bera

Performs the Jarque-Bera test for normality.

lilliefors

Performs the Lilliefors (Kolmogorov-Smirnov) test for normality.

pearson_chi_squared

Performs the Pearson chi-squared test for normality.

shapiro_wilk

Performs the Shapiro-Wilk test for normality on a given sample of data.