Struct statrs::distribution::Categorical

pub struct Categorical { /* fields omitted */ }

Implements the Categorical distribution, also known as the generalized Bernoulli or discrete distribution

Examples

use statrs::distribution::{Categorical, Discrete};
use statrs::statistics::Mean;
use statrs::prec;

let n = Categorical::new(&[0.0, 1.0, 2.0]).unwrap();
assert!(prec::almost_eq(n.mean(), 5.0 / 3.0, 1e-15));
assert_eq!(n.pmf(1), 1.0 / 3.0);

Implementations

impl Categorical

pub fn new(prob_mass: &[f64]) -> Result<Categorical>

Constructs a new categorical distribution with the probabilities masses defined by prob_mass

Errors

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

Note

The elements in prob_mass do not need to be normalized

Examples

use statrs::distribution::Categorical;

let mut result = Categorical::new(&[0.0, 1.0, 2.0]);
assert!(result.is_ok());

result = Categorical::new(&[0.0, -1.0, 2.0]);
assert!(result.is_err());

Trait Implementations

impl CheckedInverseCDF<f64> for Categorical

fn checked_inverse_cdf(&self, x: f64) -> Result<f64>

Calculates the inverse cumulative distribution function for the categorical distribution at x

Errors

If x <= 0.0 or x >= 1.0

Formula

i

where i is the first index such that x < f(i) and f(x) is defined as p_x + f(x - 1) and f(0) = p_0 where p_x is the xth probability mass

impl Clone for Categorical

fn clone(&self) -> Categorical

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Categorical

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

Formats the value using the given formatter.

impl Discrete<u64, f64> for Categorical

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

Calculates the probability mass function for the categorical distribution at x

Formula

p_x

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

Calculates the log probability mass function for the categorical distribution at x

impl Distribution<f64> for Categorical

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

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

pub fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

impl Entropy<f64> for Categorical

fn entropy(&self) -> f64

Returns the entropy of the categorical distribution

Formula

-Σ(p_j * ln(p_j))

where p_j is the jth probability mass, Σ is the sum from 0 to k - 1, and k is the number of categories

impl InverseCDF<f64> for Categorical

fn inverse_cdf(&self, x: f64) -> f64

Calculates the inverse cumulative distribution function for the categorical distribution at x

Panics

If x <= 0.0 or x >= 1.0

Formula

i

where i is the first index such that x < f(i) and f(x) is defined as p_x + f(x - 1) and f(0) = p_0 where p_x is the xth probability mass

impl Max<u64> for Categorical

fn max(&self) -> u64

Returns the maximum value in the domain of the categorical distribution representable by a 64-bit integer

Formula

n

impl Mean<f64> for Categorical

fn mean(&self) -> f64

Returns the mean of the categorical distribution

Formula

Σ(j * p_j)

where p_j is the jth probability mass, Σ is the sum from 0 to k - 1, and k is the number of categories

impl Median<f64> for Categorical

fn median(&self) -> f64

Returns the median of the categorical distribution

Formula

CDF^-1(0.5)

impl Min<u64> for Categorical

fn min(&self) -> u64

Returns the minimum value in the domain of the categorical distribution representable by a 64-bit integer

Formula

0

impl PartialEq<Categorical> for Categorical

fn eq(&self, other: &Categorical) -> bool

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

fn ne(&self, other: &Categorical) -> bool

This method tests for !=.

impl StructuralPartialEq for Categorical

impl Univariate<u64, f64> for Categorical

fn cdf(&self, x: f64) -> f64

Calculates the cumulative distribution function for the categorical distribution at x

Formula

sum(p_j) from 0..x

where p_j is the probability mass for the jth category

impl Variance<f64> for Categorical

fn variance(&self) -> f64

Returns the variance of the categorical distribution

Formula

Σ(p_j * (j - μ)^2)

where p_j is the jth probability mass, μ is the mean, Σ is the sum from 0 to k - 1, and k is the number of categories

fn std_dev(&self) -> f64

Returns the standard deviation of the categorical distribution

Formula

sqrt(Σ(p_j * (j - μ)^2))

where p_j is the jth probability mass, μ is the mean, Σ is the sum from 0 to k - 1, and k is the number of categories