Struct Multinomial 

pub struct Multinomial {
    pub n: u64,
    pub p: Array1<f64>,
}

Multinomial distribution structure

The multinomial distribution is a generalization of the binomial distribution. It models the probability of counts for each side of a k-sided die rolled n times.

Fields

n: u64

Number of trials

p: Array1<f64>

Probability of each outcome (must sum to 1)

Implementations

impl Multinomial

pub fn new<D>(n: u64, p: ArrayBase<D, Ix1>) -> StatsResult<Self>

where D: Data<Elem = f64>,

Create a new Multinomial distribution with given parameters

Arguments

• n - Number of trials
• p - Probability of each outcome (must sum to 1)

Returns

• A new Multinomial distribution instance

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

// Create a multinomial distribution for a 3-sided die rolled 10 times
let n = 10;
let p = array![0.2, 0.3, 0.5]; // Probabilities for each outcome
let multinomial = Multinomial::new(n, p).expect("Operation failed");

pub fn pmf<D>(&self, x: &ArrayBase<D, Ix1>) -> f64

where D: Data<Elem = f64>,

Calculate the probability mass function (PMF) at a given point

Arguments

• x - The point at which to evaluate the PMF (must be a vector of non-negative integers that sum to n)

Returns

• The value of the PMF at the given point

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

let n = 10;
let p = array![0.2, 0.3, 0.5];
let multinomial = Multinomial::new(n, p).expect("Operation failed");

// Calculate PMF at x = [2, 3, 5]
let x = array![2.0, 3.0, 5.0];
let pmf_value = multinomial.pmf(&x);

pub fn logpmf<D>(&self, x: &ArrayBase<D, Ix1>) -> f64

where D: Data<Elem = f64>,

Calculate the log probability mass function (log PMF) at a given point

Arguments

• x - The point at which to evaluate the log PMF (must be a vector of non-negative integers that sum to n)

Returns

• The value of the log PMF at the given point

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

let n = 10;
let p = array![0.2, 0.3, 0.5];
let multinomial = Multinomial::new(n, p).expect("Operation failed");

// Calculate log PMF at x = [2, 3, 5]
let x = array![2.0, 3.0, 5.0];
let logpmf_value = multinomial.logpmf(&x);

pub fn rvs(&self, size: usize) -> StatsResult<Vec<Array1<f64>>>

Generate random samples from the distribution

Arguments

• size - Number of samples to generate

Returns

• Vector of random samples (each sample is a vector of counts)

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

let n = 10;
let p = array![0.2, 0.3, 0.5];
let multinomial = Multinomial::new(n, p).expect("Operation failed");

// Generate 5 random samples
let samples = multinomial.rvs(5).expect("Operation failed");
assert_eq!(samples.len(), 5);
assert_eq!(samples[0].len(), 3);

pub fn rvs_single(&self) -> StatsResult<Array1<f64>>

Generate a single random sample from the distribution

Returns

• A random sample (a vector of counts)

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

let n = 10;
let p = array![0.2, 0.3, 0.5];
let multinomial = Multinomial::new(n, p).expect("Operation failed");

// Generate a single random sample
let sample = multinomial.rvs_single().expect("Operation failed");
assert_eq!(sample.len(), 3);

pub fn mean(&self) -> Array1<f64>

Calculate the mean of the distribution

Returns

• Mean vector (n * p)

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

let n = 10;
let p = array![0.2, 0.3, 0.5];
let multinomial = Multinomial::new(n, p).expect("Operation failed");

let mean = multinomial.mean();
// Mean should be [2.0, 3.0, 5.0]

pub fn cov(&self) -> Array2<f64>

Calculate the covariance matrix of the distribution

Returns

• Covariance matrix

Examples

use scirs2_core::ndarray::array;
use scirs2_stats::distributions::multivariate::multinomial::Multinomial;

let n = 10;
let p = array![0.2, 0.3, 0.5];
let multinomial = Multinomial::new(n, p).expect("Operation failed");

let cov = multinomial.cov();

Trait Implementations

impl Clone for Multinomial

fn clone(&self) -> Multinomial

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Multinomial

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

Formats the value using the given formatter.

impl SampleableDistribution<ArrayBase<OwnedRepr<f64>, Dim<[usize; 1]>>> for Multinomial

Implementation of SampleableDistribution for Multinomial

fn rvs(&self, size: usize) -> StatsResult<Vec<Array1<f64>>>

Generate random samples from the distribution