Struct Normal

pub struct Normal<F>
where
    F: Float,
    StandardNormal: Distribution<F>,
{ /* private fields */ }

The Normal distribution N(μ, σ²).

The Normal distribution, also known as the Gaussian distribution or bell curve, is a continuous probability distribution with mean μ (mu) and standard deviation σ (sigma). It is used to model continuous data that tend to cluster around a mean. The Normal distribution is symmetric and characterized by its bell-shaped curve.

See StandardNormal for an optimised implementation for μ = 0 and σ = 1.

Density function

f(x) = (1 / sqrt(2π σ²)) * exp(-((x - μ)² / (2σ²)))

Plot

The following diagram shows the Normal distribution with various values of μ and σ. The blue curve is the StandardNormal distribution, N(0, 1).

Example

use rand_distr::{Normal, Distribution};

// mean 2, standard deviation 3
let normal = Normal::new(2.0, 3.0).unwrap();
let v = normal.sample(&mut rand::rng());
println!("{} is from a N(2, 9) distribution", v)

Notes

Implemented via the ZIGNOR variant¹ of the Ziggurat method.

---

1. Jurgen A. Doornik (2005). An Improved Ziggurat Method to Generate Normal Random Samples. Nuffield College, Oxford ↩

Implementations

impl<F> Normal<F>

where F: Float, StandardNormal: Distribution<F>,

pub fn new(mean: F, std_dev: F) -> Result<Normal<F>, Error>

Construct, from mean and standard deviation

Parameters:

• mean (μ, unrestricted)
• standard deviation (σ, must be finite)

pub fn from_mean_cv(mean: F, cv: F) -> Result<Normal<F>, Error>

Construct, from mean and coefficient of variation

Parameters:

• mean (μ, unrestricted)
• coefficient of variation (cv = abs(σ / μ))

pub fn from_zscore(&self, zscore: F) -> F

Sample from a z-score

This may be useful for generating correlated samples x1 and x2 from two different distributions, as follows.

let mut rng = rand::rng();
let z = StandardNormal.sample(&mut rng);
let x1 = Normal::new(0.0, 1.0).unwrap().from_zscore(z);
let x2 = Normal::new(2.0, -3.0).unwrap().from_zscore(z);

pub fn mean(&self) -> F

Returns the mean (μ) of the distribution.

pub fn std_dev(&self) -> F

Returns the standard deviation (σ) of the distribution.

Trait Implementations

impl<F> Clone for Normal<F>

where F: Clone + Float, StandardNormal: Distribution<F>,

fn clone(&self) -> Normal<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F> Debug for Normal<F>

where F: Debug + Float, StandardNormal: Distribution<F>,

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

Formats the value using the given formatter.

impl<'de, F> Deserialize<'de> for Normal<F>

where F: Float + Deserialize<'de>, StandardNormal: Distribution<F>,

fn deserialize<__D>( __deserializer: __D, ) -> Result<Normal<F>, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F> Distribution<F> for Normal<F>

where F: Float, StandardNormal: Distribution<F>,

fn sample<R>(&self, rng: &mut R) -> F

where R: Rng + ?Sized,

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

fn sample_iter<R>(self, rng: R) -> Iter<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) -> Map<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Map sampled values to type S

impl<T> From<Normal<T>> for TruncatedNormal<T>

where T: Float, StandardNormal: Distribution<T>,

fn from(normal: Normal<T>) -> TruncatedNormal<T>

Converts to this type from the input type.

impl<F> PartialEq for Normal<F>

where F: PartialEq + Float, StandardNormal: Distribution<F>,

fn eq(&self, other: &Normal<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

const 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<F> Serialize for Normal<F>

where F: Float + Serialize, StandardNormal: Distribution<F>,

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<F> Copy for Normal<F>

where F: Copy + Float, StandardNormal: Distribution<F>,

impl<F> StructuralPartialEq for Normal<F>

where F: Float, StandardNormal: Distribution<F>,