Struct MultivariateStudent

pub struct MultivariateStudent<D>
where
    D: Dim,
    DefaultAllocator: Allocator<D> + Allocator<D, D>,
{ /* private fields */ }

Available on crate feature nalgebra only.

Implements the Multivariate Student’s t-distribution distribution using the “nalgebra” crate for matrix operations.

Assumes all the marginal distributions have the same degree of freedom, ν.

Examples

use statrs::distribution::{MultivariateStudent, Continuous};
use nalgebra::{DVector, DMatrix};
use statrs::statistics::{MeanN, VarianceN};

let mvs = MultivariateStudent::new(vec![0., 0.], vec![1., 0., 0., 1.], 4.).unwrap();
assert_eq!(mvs.mean().unwrap(), DVector::from_vec(vec![0., 0.]));
assert_eq!(mvs.variance().unwrap(), DMatrix::from_vec(2, 2, vec![2., 0., 0., 2.]));
assert_eq!(mvs.pdf(&DVector::from_vec(vec![1.,  1.])), 0.04715702017537655);

Implementations

impl MultivariateStudent<Dyn>

pub fn new( location: Vec<f64>, scale: Vec<f64>, freedom: f64, ) -> Result<Self, MultivariateStudentError>

Constructs a new multivariate students t distribution with a location of location, scale matrix scale and freedom degrees of freedom.

Errors

Returns StatsError::BadParams if the scale matrix is not symmetric-positive definite and StatsError::ArgMustBePositive if freedom is non-positive.

pub fn dim(&self) -> usize

Returns the dimension of the distribution.

impl<D> MultivariateStudent<D>

where D: DimMin<D, Output = D>, DefaultAllocator: Allocator<D> + Allocator<D, D>,

pub fn new_from_nalgebra( location: OVector<f64, D>, scale: OMatrix<f64, D, D>, freedom: f64, ) -> Result<Self, MultivariateStudentError>

pub fn scale_chol_decomp(&self) -> &OMatrix<f64, D, D>

Returns the cholesky decomposiiton matrix of the scale matrix.

Returns A where Σ = AAᵀ.

pub fn location(&self) -> &OVector<f64, D>

Returns the location of the distribution.

pub fn scale(&self) -> &OMatrix<f64, D, D>

Returns the scale matrix of the distribution.

pub fn freedom(&self) -> f64

Returns the degrees of freedom of the distribution.

pub fn precision(&self) -> &OMatrix<f64, D, D>

Returns the inverse of the cholesky decomposition matrix.

pub fn ln_pdf_const(&self) -> f64

Returns the logarithmed constant part of the probability distribution function.

Trait Implementations

impl<D> Clone for MultivariateStudent<D>

where D: Dim + Clone, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn clone(&self) -> MultivariateStudent<D>

Returns a copy of the value.

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

Performs copy-assignment from source.

impl<D> Continuous<&Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>, f64> for MultivariateStudent<D>

where D: Dim + DimMin<D, Output = D>, DefaultAllocator: Allocator<D> + Allocator<D, D>,

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

Calculates the probability density function for the multivariate. student distribution at x.

Formula

[Γ(ν+p)/2] / [Γ(ν/2) ((ν * π)^p det(Σ))^(1 / 2)] * [1 + 1/ν (x - μ)ᵀ inv(Σ) (x - μ)]^(-(ν+p)/2)

where

• ν is the degrees of freedom,
• μ is the mean,
• Γ is the Gamma function,
• inv(Σ) is the precision matrix,
• det(Σ) is the determinant of the scale matrix, and
• k is the dimension of the distribution.

fn ln_pdf(&self, x: &OVector<f64, D>) -> f64

Calculates the log probability density function for the multivariate student distribution at x. Equivalent to pdf(x).ln().

impl<D> Debug for MultivariateStudent<D>

where D: Dim + Debug, DefaultAllocator: Allocator<D> + Allocator<D, D>,

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

Formats the value using the given formatter.

impl<D> Distribution<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

Available on crate feature rand only.

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> OVector<f64, D>

Samples from the multivariate student distribution

Formula

W ⋅ L ⋅ Z + μ

where W has √(ν/Sν) distribution, Sν has Chi-squared distribution with ν degrees of freedom, L is the Cholesky decomposition of the scale matrix, Z is a vector of normally distributed random variables, and μ is the location vector

fn sample_iter<R>(self, rng: R) -> DistIter<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) -> DistMap<Self, F, T, S>

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

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl<D> Max<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn max(&self) -> OVector<f64, D>

Returns the minimum value in the domain of the multivariate normal distribution represented by a real vector

impl<D> MeanN<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn mean(&self) -> Option<OVector<f64, D>>

Returns the mean of the student distribution.

Remarks

This is the same mean used to construct the distribution if the degrees of freedom is larger than 1.

impl<D> Min<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn min(&self) -> OVector<f64, D>

Returns the minimum value in the domain of the multivariate normal distribution represented by a real vector

impl<D> Mode<Matrix<f64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<f64>>> for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn mode(&self) -> OVector<f64, D>

Returns the mode of the multivariate student distribution.

Formula

μ

where μ is the location.

impl<D> PartialEq for MultivariateStudent<D>

where D: Dim + PartialEq, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn eq(&self, other: &MultivariateStudent<D>) -> 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<D> VarianceN<Matrix<f64, D, D, <DefaultAllocator as Allocator<D, D>>::Buffer<f64>>> for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,

fn variance(&self) -> Option<OMatrix<f64, D, D>>

Returns the covariance matrix of the multivariate student distribution.

Formula

Σ ⋅ ν / (ν - 2)

where Σ is the scale matrix and ν is the degrees of freedom. Only defined if freedom is larger than 2.

impl<D> StructuralPartialEq for MultivariateStudent<D>

where D: Dim, DefaultAllocator: Allocator<D> + Allocator<D, D>,