Struct statrs::distribution::Dirichlet

pub struct Dirichlet { /* fields omitted */ }

Implements the Dirichlet distribution

Examples

use statrs::distribution::{Dirichlet, Continuous};
use statrs::statistics::Mean;

let n = Dirichlet::new(&[1.0, 2.0, 3.0]).unwrap();
assert_eq!(n.mean(), [1.0 / 6.0, 1.0 / 3.0, 0.5]);
assert_eq!(n.pdf(&[0.33333, 0.33333, 0.33333]), 2.222155556222205);

Methods

impl Dirichlet

fn new(alpha: &[f64]) -> Result<Dirichlet>

Constructs a new dirichlet distribution with the given concenctration parameters (alpha)

Errors

Returns an error if any element x in alpha exist such that x < = 0.0 or x is NaN, or if the length of alpha is less than 2

Examples

use statrs::distribution::Dirichlet;

let alpha_ok = [1.0, 2.0, 3.0];
let mut result = Dirichlet::new(&alpha_ok);
assert!(result.is_ok());

let alpha_err = [0.0];
result = Dirichlet::new(&alpha_err);
assert!(result.is_err());

fn new_with_param(alpha: f64, n: usize) -> Result<Dirichlet>

Constructs a new dirichlet distribution with the given concenctration parameter (alpha) repeated n times

Errors

Returns an error if alpha < = 0.0 or alpha is NaN, or if n < 2

Examples

use statrs::distribution::Dirichlet;

let mut result = Dirichlet::new_with_param(1.0, 3);
assert!(result.is_ok());

result = Dirichlet::new_with_param(0.0, 1);
assert!(result.is_err());

fn alpha(&self) -> &[f64]

Returns the concentration parameters of the dirichlet distribution as a slice

Examples

use statrs::distribution::Dirichlet;

let n = Dirichlet::new(&[1.0, 2.0, 3.0]).unwrap();
assert_eq!(n.alpha(), [1.0, 2.0, 3.0]);

Trait Implementations

impl Debug for Dirichlet

fn fmt(&self, __arg_0: &mut Formatter) -> Result

Formats the value using the given formatter.

impl Clone for Dirichlet

fn clone(&self) -> Dirichlet

Returns a copy of the value.

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

Performs copy-assignment from source.

impl PartialEq for Dirichlet

fn eq(&self, __arg_0: &Dirichlet) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, __arg_0: &Dirichlet) -> bool

This method tests for !=.

impl Sample<Vec<f64>> for Dirichlet

fn sample<R: Rng>(&mut self, r: &mut R) -> Vec<f64>

Generate random samples from a dirichlet distribution using r as the source of randomness. Refer here for implementation details

impl IndependentSample<Vec<f64>> for Dirichlet

fn ind_sample<R: Rng>(&self, r: &mut R) -> Vec<f64>

Generate random independent samples from a dirichlet distribution using r as the source of randomness. Refer here for implementation details

impl Distribution<Vec<f64>> for Dirichlet

fn sample<R: Rng>(&self, r: &mut R) -> Vec<f64>

Generate random samples from the dirichlet distribution using r as the source of randomness

Examples

use rand::StdRng;
use statrs::distribution::{Dirichlet, Distribution};

let mut r = rand::StdRng::new().unwrap();
let n = Dirichlet::new(&[1.0, 2.0, 3.0]).unwrap();
print!("{:?}", n.sample::<StdRng>(&mut r));

impl Mean<Vec<f64>> for Dirichlet

fn mean(&self) -> Vec<f64>

Returns the means of the dirichlet distribution

Formula

α_i / α_0

for the ith element where α_i is the ith concentration parameter and α_0 is the sum of all concentration parameters

impl Variance<Vec<f64>> for Dirichlet

fn variance(&self) -> Vec<f64>

Returns the variances of the dirichlet distribution

Formula

(α_i * (α_0 - α_i)) / (α_0^2 * (α_0 + 1))

for the ith element where α_i is the ith concentration parameter and α_0 is the sum of all concentration parameters

fn std_dev(&self) -> Vec<f64>

Returns the standard deviation of the dirichlet distribution

Formula

sqrt((α_i * (α_0 - α_i)) / (α_0^2 * (α_0 + 1)))

for the ith element where α_i is the ith concentration parameter and α_0 is the sum of all concentration parameters

impl Entropy<f64> for Dirichlet

fn entropy(&self) -> f64

Returns the entropy of the dirichlet distribution

Formula

ln(B(α)) - (K - α_0)ψ(α_0) - Σ((α_i - 1)ψ(α_i))

where

B(α) = Π(Γ(α_i)) / Γ(Σ(α_i))

α_0 is the sum of all concentration parameters, K is the number of concentration parameters, ψ is the digamma function, α_i is the ith concentration parameter, and Σ is the sum from 1 to K

impl<'a> Continuous<&'a [f64], f64> for Dirichlet

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

Calculates the probabiliy density function for the dirichlet distribution with given x's corresponding to the concentration parameters for this distribution

Panics

If any element in x is not in (0, 1), the elements in x do not sum to 1 with a tolerance of 1e-4, or if x is not the same length as the vector of concentration parameters for this distribution

Formula

(1 / B(α)) * Π(x_i^(α_i - 1))

where

B(α) = Π(Γ(α_i)) / Γ(Σ(α_i))

α is the vector of concentration parameters, α_i is the ith concentration parameter, x_i is the ith argument corresponding to the ith concentration parameter, Γ is the gamma function, Π is the product from 1 to K, Σ is the sum from 1 to K, and K is the number of concentration parameters

fn ln_pdf(&self, x: &[f64]) -> f64

Calculates the log probabiliy density function for the dirichlet distribution with given x's corresponding to the concentration parameters for this distribution

Panics

If any element in x is not in (0, 1), the elements in x do not sum to 1 with a tolerance of 1e-4, or if x is not the same length as the vector of concentration parameters for this distribution

Formula

ln((1 / B(α)) * Π(x_i^(α_i - 1)))

where

B(α) = Π(Γ(α_i)) / Γ(Σ(α_i))

α is the vector of concentration parameters, α_i is the ith concentration parameter, x_i is the ith argument corresponding to the ith concentration parameter, Γ is the gamma function, Π is the product from 1 to K, Σ is the sum from 1 to K, and K is the number of concentration parameters