Struct Multinomial

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

Implements the Multinomial distribution which is a generalization of the Binomial distribution

Examples

use statrs::distribution::Multinomial;
use statrs::statistics::MeanN;
use nalgebra::vector;

let n = Multinomial::new_from_nalgebra(vector![0.3, 0.7], 5).unwrap();
assert_eq!(n.mean().unwrap(), (vector![1.5, 3.5]));

Implementations

impl Multinomial<Dyn>

pub fn new(p: Vec<f64>, n: u64) -> Result<Self, MultinomialError>

Constructs a new multinomial distribution with probabilities p and n number of trials.

Errors

Returns an error if p is empty, the sum of the elements in p is 0, or any element in p is less than 0 or is f64::NAN

Note

The elements in p do not need to be normalized

Examples

use statrs::distribution::Multinomial;

let mut result = Multinomial::new(vec![0.0, 1.0, 2.0], 3);
assert!(result.is_ok());

result = Multinomial::new(vec![0.0, -1.0, 2.0], 3);
assert!(result.is_err());

impl<D> Multinomial<D>

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

pub fn new_from_nalgebra( p: OVector<f64, D>, n: u64, ) -> Result<Self, MultinomialError>

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

Returns the probabilities of the multinomial distribution as a slice

Examples

use statrs::distribution::Multinomial;
use nalgebra::dvector;

let n = Multinomial::new(vec![0.0, 1.0, 2.0], 3).unwrap();
assert_eq!(*n.p(), dvector![0.0, 1.0/3.0, 2.0/3.0]);

pub fn n(&self) -> u64

Returns the number of trials of the multinomial distribution

Examples

use statrs::distribution::Multinomial;

let n = Multinomial::new(vec![0.0, 1.0, 2.0], 3).unwrap();
assert_eq!(n.n(), 3);

Trait Implementations

impl<D> Clone for Multinomial<D>

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

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

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<D> Debug for Multinomial<D>

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

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

Formats the value using the given formatter.

impl<D> Discrete<&Matrix<u64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<u64>>, f64> for Multinomial<D>

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

fn pmf(&self, x: &OVector<u64, D>) -> f64

Calculates the probability mass function for the multinomial distribution with the given x’s corresponding to the probabilities for this distribution

Panics

If length of x is not equal to length of p

Formula

(n! / x_1!...x_k!) * p_i^x_i for i in 1...k

where n is the number of trials, p_i is the ith probability, x_i is the ith x value, and k is the total number of probabilities

fn ln_pmf(&self, x: &OVector<u64, D>) -> f64

Calculates the log probability mass function for the multinomial distribution with the given x’s corresponding to the probabilities for this distribution

Panics

If length of x is not equal to length of p

Formula

ln((n! / x_1!...x_k!) * p_i^x_i) for i in 1...k

where n is the number of trials, p_i is the ith probability, x_i is the ith x value, and k is the total number of probabilities

impl<D> Display for Multinomial<D>

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

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

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

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

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> Distribution<Matrix<u64, D, Const<1>, <DefaultAllocator as Allocator<D>>::Buffer<u64>>> for Multinomial<D>

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

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> OVector<u64, D>

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

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

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

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

Returns the mean of the multinomial distribution

Formula

n * p_i for i in 1...k

where n is the number of trials, p_i is the ith probability, and k is the total number of probabilities

impl<D> PartialEq for Multinomial<D>

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

fn eq(&self, other: &Multinomial<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 Multinomial<D>

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

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

Returns the variance of the multinomial distribution

Formula

n * p_i * (1 - p_i) for i in 1...k

where n is the number of trials, p_i is the ith probability, and k is the total number of probabilities

impl<D> StructuralPartialEq for Multinomial<D>

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