# Struct rand_distr::Normal

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

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();
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§

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### impl<F> Normal<F>where F: Float, StandardNormal: Distribution<F>,

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#### 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)
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#### 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)`)
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#### 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 = thread_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);``````
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#### pub fn mean(&self) -> F

Returns the mean (`μ`) of the distribution.

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#### pub fn std_dev(&self) -> F

Returns the standard deviation (`σ`) of the distribution.

## Trait Implementations§

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### impl<F> Clone for Normal<F>where F: Float + Clone, StandardNormal: Distribution<F>,

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

Returns a copy of the value. Read more
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#### fn clone_from(&mut self, source: &Self)

Performs copy-assignment from `source`. Read more
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### impl<F> Debug for Normal<F>where F: Float + Debug, StandardNormal: Distribution<F>,

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

Formats the value using the given formatter. Read more
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### impl<'de, F> Deserialize<'de> for Normal<F>where F: Float + Deserialize<'de>, StandardNormal: Distribution<F>,

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#### fn deserialize<__D>(__deserializer: __D) -> Result<Self, __D::Error>where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer. Read more
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### impl<F> Distribution<F> for Normal<F>where F: Float, StandardNormal: Distribution<F>,

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

Generate a random value of `T`, using `rng` as the source of randomness.
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#### 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. Read more
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#### 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` Read more
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### impl<F> PartialEq for Normal<F>where F: Float + PartialEq, StandardNormal: Distribution<F>,

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

Tests for `self` and `other` values to be equal, and is used by `==`.
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#### fn ne(&self, other: &Rhs) -> bool

Tests for `!=`. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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### impl<F> Serialize for Normal<F>where F: Float + Serialize, StandardNormal: Distribution<F>,

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

Serialize this value into the given Serde serializer. Read more
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## Blanket Implementations§

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### impl<T> Any for Twhere T: 'static + ?Sized,

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#### fn type_id(&self) -> TypeId

Gets the `TypeId` of `self`. Read more
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### impl<T> Borrow<T> for Twhere T: ?Sized,

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#### fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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### impl<T> BorrowMut<T> for Twhere T: ?Sized,

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#### fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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### impl<T> CloneToUninit for Twhere T: Clone,

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#### unsafe fn clone_to_uninit(&self, dst: *mut T)

🔬This is a nightly-only experimental API. (`clone_to_uninit`)
Performs copy-assignment from `self` to `dst`. Read more
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### impl<T> From<T> for T

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#### fn from(t: T) -> T

Returns the argument unchanged.

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### impl<T, U> Into<U> for Twhere U: From<T>,

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#### fn into(self) -> U

Calls `U::from(self)`.

That is, this conversion is whatever the implementation of `From<T> for U` chooses to do.

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### impl<T> ToOwned for Twhere T: Clone,

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#### type Owned = T

The resulting type after obtaining ownership.
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#### fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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#### fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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### impl<T, U> TryFrom<U> for Twhere U: Into<T>,

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#### type Error = Infallible

The type returned in the event of a conversion error.
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#### fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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### impl<T, U> TryInto<U> for Twhere U: TryFrom<T>,

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#### type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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#### fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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