# [−][src]Struct statrs::distribution::Normal

`pub struct Normal { /* fields omitted */ }`

Implements the Normal distribution

# Examples

```use statrs::distribution::{Normal, Continuous};
use statrs::statistics::Mean;

let n = Normal::new(0.0, 1.0).unwrap();
assert_eq!(n.mean(), 0.0);
assert_eq!(n.pdf(1.0), 0.2419707245191433497978);```

## Methods

### `impl Normal`[src]

#### `pub fn new(mean: f64, std_dev: f64) -> Result<Normal>`[src]

Constructs a new normal distribution with a mean of `mean` and a standard deviation of `std_dev`

# Errors

Returns an error if `mean` or `std_dev` are `NaN` or if `std_dev <= 0.0`

# Examples

```use statrs::distribution::Normal;

let mut result = Normal::new(0.0, 1.0);
assert!(result.is_ok());

result = Normal::new(0.0, 0.0);
assert!(result.is_err());```

## Trait Implementations

### `impl Univariate<f64, f64> for Normal`[src]

#### `fn cdf(&self, x: f64) -> f64`[src]

Calculates the cumulative distribution function for the normal distribution at `x`

# Formula

`(1 / 2) * (1 + erf((x - μ) / (σ * sqrt(2))))`

where `μ` is the mean, `σ` is the standard deviation, and `erf` is the error function

### `impl InverseCDF<f64> for Normal`[src]

#### `fn inverse_cdf(&self, x: f64) -> f64`[src]

Calculates the inverse cumulative distribution function for the normal distribution at `x`

# Panics

If `x < 0.0` or `x > 1.0`

# Formula

`μ - sqrt(2) * σ * erfc_inv(2x)`

where `μ` is the mean, `σ` is the standard deviation and `erfc_inv` is the inverse of the complementary error function

### `impl CheckedInverseCDF<f64> for Normal`[src]

#### `fn checked_inverse_cdf(&self, x: f64) -> Result<f64>`[src]

Calculates the inverse cumulative distribution function for the normal distribution at `x`

# Errors

If `x < 0.0` or `x > 1.0`

# Formula

`μ - sqrt(2) * σ * erfc_inv(2x)`

where `μ` is the mean, `σ` is the standard deviation and `erfc_inv` is the inverse of the complementary error function

### `impl Continuous<f64, f64> for Normal`[src]

#### `fn pdf(&self, x: f64) -> f64`[src]

Calculates the probability density function for the normal distribution at `x`

# Formula

`(1 / sqrt(2σ^2 * π)) * e^(-(x - μ)^2 / 2σ^2)`

where `μ` is the mean and `σ` is the standard deviation

#### `fn ln_pdf(&self, x: f64) -> f64`[src]

Calculates the log probability density function for the normal distribution at `x`

# Formula

`ln((1 / sqrt(2σ^2 * π)) * e^(-(x - μ)^2 / 2σ^2))`

where `μ` is the mean and `σ` is the standard deviation

### `impl Min<f64> for Normal`[src]

#### `fn min(&self) -> f64`[src]

Returns the minimum value in the domain of the normal distribution representable by a double precision float

# Formula

`-INF`

### `impl Max<f64> for Normal`[src]

#### `fn max(&self) -> f64`[src]

Returns the maximum value in the domain of the normal distribution representable by a double precision float

# Formula

`INF`

### `impl Mean<f64> for Normal`[src]

#### `fn mean(&self) -> f64`[src]

Returns the mean of the normal distribution

# Remarks

This is the same mean used to construct the distribution

### `impl Variance<f64> for Normal`[src]

#### `fn variance(&self) -> f64`[src]

Returns the variance of the normal distribution

# Formula

`σ^2`

where `σ` is the standard deviation

#### `fn std_dev(&self) -> f64`[src]

Returns the standard deviation of the normal distribution

# Remarks

This is the same standard deviation used to construct the distribution

### `impl Entropy<f64> for Normal`[src]

#### `fn entropy(&self) -> f64`[src]

Returns the entropy of the normal distribution

# Formula

`(1 / 2) * ln(2σ^2 * π * e)`

where `σ` is the standard deviation

### `impl Skewness<f64> for Normal`[src]

#### `fn skewness(&self) -> f64`[src]

Returns the skewness of the normal distribution

# Formula

`0`

### `impl Median<f64> for Normal`[src]

#### `fn median(&self) -> f64`[src]

Returns the median of the normal distribution

# Formula

`μ`

where `μ` is the mean

### `impl Mode<f64> for Normal`[src]

#### `fn mode(&self) -> f64`[src]

Returns the mode of the normal distribution

# Formula

`μ`

where `μ` is the mean

### `impl Clone for Normal`[src]

#### `fn clone_from(&mut self, source: &Self)`1.0.0[src]

Performs copy-assignment from `source`. Read more

### `impl Distribution<f64> for Normal`[src]

#### `fn sample_iter<R>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T> where    R: Rng, `[src]

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

## Blanket Implementations

### `impl<T> ToOwned for T where    T: Clone, `[src]

#### `type Owned = T`

The resulting type after obtaining ownership.

### `impl<T, U> TryFrom<U> for T where    U: Into<T>, `[src]

#### `type Error = Infallible`

The type returned in the event of a conversion error.

### `impl<T, U> TryInto<U> for T where    U: TryFrom<T>, `[src]

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

The type returned in the event of a conversion error.