Struct Gaussian 

pub struct Gaussian { /* private fields */ }

Gaussian (normal) distribution: X ~ N(mu, sigma^2) https://en.wikipedia.org/wiki/Normal_distribution

Implementations

impl Gaussian

pub const fn new(mean: f64, variance: f64) -> Gaussian

New instance of a Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.cf(5.0).re, 3.7266532e-6, 1e-7);
assert_eq!(gaussian.cf(5.0).im, 0.0);

Panics

Panics if variance is not positive.

Trait Implementations

impl Default for Gaussian

fn default() -> Gaussian

Returns the “default value” for a type.

impl Distribution for Gaussian

fn cf(&self, t: f64) -> Complex<f64>

Characteristic function of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.cf(5.0).re, 3.7266532e-6, 1e-7);
assert_eq!(gaussian.cf(5.0).im, 0.0);

fn pdf(&self, x: f64) -> f64

Probability density function of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.pdf(1.0), 0.2419707, 1e-7);

fn pmf(&self, x: f64) -> f64

Probability mass function for the Gaussian distribution (continuous) is not defined. Using this method will call self.pdf() instead.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.pmf(1.0), gaussian.pdf(1.0), 1e-7);

fn cdf(&self, x: f64) -> f64

Cumulative distribution function of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.cdf(1.0), 0.8413447, 1e-7);
assert_approx_equal!(gaussian.cdf(-1.0), 0.1586553, 1e-7);

fn inv_cdf(&self, p: f64) -> f64

Inverse distribution (quantile) function of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.inv_cdf(0.5), 0.0);
assert_approx_equal!(gaussian.inv_cdf(0.001), -3.090232306167813, f64::EPSILON);
assert_approx_equal!(gaussian.inv_cdf(0.997), 2.747781385444993, f64::EPSILON);

fn mean(&self) -> f64

Returns the mean of the Gaussian distribution. The mean of the Gaussian distribution is equal to its median.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.mean(), 0.0);

fn median(&self) -> f64

Returns the median of the Gaussian distribution. The median of the Gaussian distribution is equal to its mean.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.median(), gaussian.mean());

fn mode(&self) -> f64

Returns the mode of the Gaussian distribution. The mode of the Gaussian distribution is equal to its mean.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.mode(), gaussian.mean());

fn variance(&self) -> f64

Returns the variance of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.variance(), 1.0);

fn skewness(&self) -> f64

Returns the skewness of the Gaussian distribution. The skewness of the Gaussian distribution is equal to 0.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.skewness(), 0.0);

fn kurtosis(&self) -> f64

Returns the kurtosis of the Gaussian distribution. The kurtosis of the Gaussian distribution is equal to 0.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_eq!(gaussian.kurtosis(), 0.0);

fn entropy(&self) -> f64

Returns the entropy of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.entropy(), 1.4189385, 1e-7);

fn mgf(&self, t: f64) -> f64

Returns the moment generating function of the Gaussian distribution.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

assert_approx_equal!(gaussian.mgf(1.0), 1.6487213, 1e-7);

fn sample(&self, n: usize) -> Result<Vec<f64>, RustQuantError>

Generates a random sample from the Gaussian distribution using the Standard Normal Random Variates Generator.

Examples

let gaussian = Gaussian::new(0.0, 1.0);

let sample = gaussian.sample(1000).expect("Gaussian sampled");
let mean = sample.iter().sum::<f64>() / sample.len() as f64;

assert_approx_equal!(mean, gaussian.mean(), 0.1);