RustQuant 0.0.4

A Rust library for quantitative finance tools.
Documentation 
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#![deny(missing_docs)]

use {
    rand::thread_rng,
    rand_distr::{Distribution, Normal},
    statrs::function::erf,
    std::f64::consts::{PI, SQRT_2},
};

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// STANDARD NORMAL DISTRIBUTION STRUCT
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

/// Base struct for a Standard Normal distribution.
/// Gaussian with mean = 0, variance = 1.
#[derive(Debug)]
pub struct StandardNormal {}

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// FUNCTIONS
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

impl Default for StandardNormal {
    fn default() -> Self {
        Self::new()
    }
}

impl StandardNormal {
    /// New standard normal distribution.
    pub fn new() -> Self {
        Self {}
    }

    /// Standard Normal Density Function
    pub fn pdf(&self, x: f64) -> f64 {
        (-x * x / 2.0).exp() / (2.0 * PI).sqrt()
    }

    /// Standard Normal Distribution Function
    ///
    /// I used `erfc` (complementary error function) instead of `erf` to avoid
    /// subtractive cancellation that leads to inaccuracy in the tails.
    pub fn cdf(&self, x: f64) -> f64 {
        0.5 * erf::erfc(-x / SQRT_2)
    }

    /// Standard Normal Random Variates Generator
    pub fn variates(&self, n: usize) -> Vec<f64> {
        let mut rng = thread_rng();
        let normal = Normal::new(0.0, 1.0).unwrap();
        let mut variates: Vec<f64> = Vec::with_capacity(n);

        for _ in 0..variates.capacity() {
            variates.push(normal.sample(&mut rng));
        }

        variates
    }
}

// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
// TESTS
// ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#[cfg(test)]
mod tests {
    use super::*;
    use crate::assert_approx_equal;

    #[test]
    fn test_pnorm() {
        let normal = StandardNormal::new();

        // Values from WolframAlpha
        assert_approx_equal!(normal.cdf(-4.0), 0.00003167, 1e-8);
        assert_approx_equal!(normal.cdf(-3.0), 0.00134990, 1e-8);
        assert_approx_equal!(normal.cdf(-2.0), 0.02275013, 1e-8);
        assert_approx_equal!(normal.cdf(-1.0), 0.15865525, 1e-8);
        assert_approx_equal!(normal.cdf(0.0), 0.5, 1e-8);
        assert_approx_equal!(normal.cdf(1.0), 0.84134475, 1e-8);
        assert_approx_equal!(normal.cdf(2.0), 0.97724987, 1e-8);
        assert_approx_equal!(normal.cdf(3.0), 0.99865010, 1e-8);
        assert_approx_equal!(normal.cdf(4.0), 0.99996833, 1e-8);
    }

    #[test]
    fn test_dnorm() {
        let normal = StandardNormal::new();

        // Values from WolframAlpha
        assert_approx_equal!(normal.pdf(-4.0), 0.00013383, 1e-8);
        assert_approx_equal!(normal.pdf(-3.0), 0.00443185, 1e-8);
        assert_approx_equal!(normal.pdf(-2.0), 0.05399097, 1e-8);
        assert_approx_equal!(normal.pdf(-1.0), 0.24197072, 1e-8);
        assert_approx_equal!(normal.pdf(0.0), 0.39894228, 1e-8);
        assert_approx_equal!(normal.pdf(1.0), 0.24197072, 1e-8);
        assert_approx_equal!(normal.pdf(2.0), 0.05399097, 1e-8);
        assert_approx_equal!(normal.pdf(3.0), 0.00443185, 1e-8);
        assert_approx_equal!(normal.pdf(4.0), 0.00013383, 1e-8);
    }

    #[test]
    fn test_rnorm() {
        let normal = StandardNormal::new();

        let v = normal.variates(1000);

        println!("{:?}", v);
        let mean = (v.iter().sum::<f64>()) / (v.len() as f64);
        println!("MEAN = {}", mean);
        // assert!(5 == 6);
    }
}