Struct statrs::distribution::Categorical

pub struct Categorical { /* private fields */ }

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

Examples

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

let n = Categorical::new(&[0.0, 1.0, 2.0]).unwrap();
assert!(prec::almost_eq(n.mean().unwrap(), 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 Clone for Categorical

fn clone(&self) -> Categorical

Returns a copy of the value.

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 DiscreteCDF<u64, f64> for Categorical

fn cdf(&self, x: u64) -> 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

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

Calculates the survival function for the categorical distribution at x

Formula

[ sum(p_j) from x..end ]

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

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 Distribution<f64> for Categorical

fn mean(&self) -> Option<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

fn variance(&self) -> Option<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 entropy(&self) -> Option<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

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

fn skewness(&self) -> Option<T>

Returns the skewness, if it exists.

impl Distribution<f64> for Categorical

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

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 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 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 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: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl StructuralPartialEq for Categorical