pub struct SkewNormal<F>{ /* private fields */ }
Expand description
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§
source§impl<F> SkewNormal<F>
impl<F> SkewNormal<F>
sourcepub fn new(location: F, scale: F, shape: F) -> Result<SkewNormal<F>, Error>
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)
Trait Implementations§
source§impl<F> Clone for SkewNormal<F>
impl<F> Clone for SkewNormal<F>
source§fn clone(&self) -> SkewNormal<F>
fn clone(&self) -> SkewNormal<F>
1.0.0 · source§fn clone_from(&mut self, source: &Self)
fn clone_from(&mut self, source: &Self)
source
. Read moresource§impl<F> Debug for SkewNormal<F>
impl<F> Debug for SkewNormal<F>
source§impl<'de, F> Deserialize<'de> for SkewNormal<F>
impl<'de, F> Deserialize<'de> for SkewNormal<F>
source§fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where
__D: Deserializer<'de>,
fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where
__D: Deserializer<'de>,
source§impl<F> Distribution<F> for SkewNormal<F>
impl<F> Distribution<F> for SkewNormal<F>
source§impl<F> PartialEq for SkewNormal<F>
impl<F> PartialEq for SkewNormal<F>
source§impl<F> Serialize for SkewNormal<F>
impl<F> Serialize for SkewNormal<F>
impl<F> Copy for SkewNormal<F>
impl<F> StructuralPartialEq for SkewNormal<F>
Auto Trait Implementations§
impl<F> Freeze for SkewNormal<F>where
F: Freeze,
impl<F> RefUnwindSafe for SkewNormal<F>where
F: RefUnwindSafe,
impl<F> Send for SkewNormal<F>where
F: Send,
impl<F> Sync for SkewNormal<F>where
F: Sync,
impl<F> Unpin for SkewNormal<F>where
F: Unpin,
impl<F> UnwindSafe for SkewNormal<F>where
F: UnwindSafe,
Blanket Implementations§
source§impl<T> BorrowMut<T> for Twhere
T: ?Sized,
impl<T> BorrowMut<T> for Twhere
T: ?Sized,
source§fn borrow_mut(&mut self) -> &mut T
fn borrow_mut(&mut self) -> &mut T
source§impl<T> CloneToUninit for Twhere
T: Clone,
impl<T> CloneToUninit for Twhere
T: Clone,
source§unsafe fn clone_to_uninit(&self, dst: *mut T)
unsafe fn clone_to_uninit(&self, dst: *mut T)
clone_to_uninit
)