# Struct rand_distr::Normal

source · `pub struct Normal<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();
let v = normal.sample(&mut rand::thread_rng());
println!("{} is from a N(2, 9) distribution", v)
```

## §Notes

Implemented via the ZIGNOR variant^{1} of the Ziggurat method.

Jurgen A. Doornik (2005).

*An Improved Ziggurat Method to Generate Normal Random Samples*. Nuffield College, Oxford ↩

## Implementations§

source§### impl<F> Normal<F>

### impl<F> Normal<F>

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

#### 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)

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

#### 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)`

)

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

#### 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);
```

## Trait Implementations§

source§### impl<'de, F> Deserialize<'de> for Normal<F>

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

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

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

source§### impl<F> Distribution<F> for Normal<F>

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

### impl<F> Copy for Normal<F>

### impl<F> StructuralPartialEq for Normal<F>

## Auto Trait Implementations§

### impl<F> Freeze for Normal<F>where
F: Freeze,

### impl<F> RefUnwindSafe for Normal<F>where
F: RefUnwindSafe,

### impl<F> Send for Normal<F>where
F: Send,

### impl<F> Sync for Normal<F>where
F: Sync,

### impl<F> Unpin for Normal<F>where
F: Unpin,

### impl<F> UnwindSafe for Normal<F>where
F: UnwindSafe,

## Blanket Implementations§

source§### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

### impl<T> BorrowMut<T> for Twhere
T: ?Sized,

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

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

source§### impl<T> CloneToUninit for Twhere
T: Clone,

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

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

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

`clone_to_uninit`

)