Struct SkewNormal 

pub struct SkewNormal<F>
where
    F: Float,
    StandardNormal: Distribution<F>,
{ /* private fields */ }

The skew normal distribution SN(ξ, ω, α).

The skew normal distribution is a generalization of the Normal distribution to allow for non-zero skewness. It has location parameter ξ (xi), scale parameter ω (omega), and shape parameter α (alpha).

The ξ and ω parameters correspond to the mean μ and standard deviation σ of the normal distribution, respectively. The α parameter controls the skewness.

Density function

It has the density function, for scale > 0, f(x) = 2 / scale * phi((x - location) / scale) * Phi(alpha * (x - location) / scale) where phi and Phi are the density and distribution of a standard normal variable.

Plot

The following plot shows the skew normal distribution with location = 0, scale = 1 (corresponding to the standard normal distribution), and various values of shape.

Example

use rand_distr::{SkewNormal, Distribution};

// location 2, scale 3, shape 1
let skew_normal = SkewNormal::new(2.0, 3.0, 1.0).unwrap();
let v = skew_normal.sample(&mut rand::rng());
println!("{} is from a SN(2, 3, 1) distribution", v)

Implementation details

We are using the algorithm from A Method to Simulate the Skew Normal Distribution.

Implementations

impl<F> SkewNormal<F>

where F: Float, StandardNormal: Distribution<F>,

pub fn new(location: F, scale: F, shape: F) -> Result<SkewNormal<F>, Error>

Construct, from location, scale and shape.

Parameters:

• location (unrestricted)
• scale (must be finite and larger than zero)
• shape (must be finite)

pub fn location(&self) -> F

Returns the location of the distribution.

pub fn scale(&self) -> F

Returns the scale of the distribution.

pub fn shape(&self) -> F

Returns the shape of the distribution.

Trait Implementations

impl<F> Clone for SkewNormal<F>

where F: Clone + Float, StandardNormal: Distribution<F>,

fn clone(&self) -> SkewNormal<F>

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F> Debug for SkewNormal<F>

where F: Debug + Float, StandardNormal: Distribution<F>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result<(), Error>

Formats the value using the given formatter.

impl<F> Distribution<F> for SkewNormal<F>

where F: Float, StandardNormal: Distribution<F>,

fn sample<R>(&self, rng: &mut R) -> F

where R: Rng + ?Sized,

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> Iter<Self, R, T>

where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl<F> PartialEq for SkewNormal<F>

where F: PartialEq + Float, StandardNormal: Distribution<F>,

fn eq(&self, other: &SkewNormal<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F> Copy for SkewNormal<F>

where F: Copy + Float, StandardNormal: Distribution<F>,

impl<F> StructuralPartialEq for SkewNormal<F>

where F: Float, StandardNormal: Distribution<F>,