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

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

Implements the Cauchy distribution, also known as the Lorentz distribution.

# Examples

```use statrs::distribution::{Cauchy, Continuous};
use statrs::statistics::Mode;

let n = Cauchy::new(0.0, 1.0).unwrap();
assert_eq!(n.mode(), 0.0);
assert_eq!(n.pdf(1.0), 0.1591549430918953357689);```

## Methods

### `impl Cauchy`[src]

#### `pub fn new(location: f64, scale: f64) -> Result<Cauchy>`[src]

Constructs a new cauchy distribution with the given location and scale.

# Errors

Returns an error if location or scale are `NaN` or `scale <= 0.0`

# Examples

```use statrs::distribution::Cauchy;

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

result = Cauchy::new(0.0, -1.0);
assert!(result.is_err());```

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

Returns the location of the cauchy distribution

# Examples

```use statrs::distribution::Cauchy;

let n = Cauchy::new(0.0, 1.0).unwrap();
assert_eq!(n.location(), 0.0);```

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

Returns the scale of the cauchy distribution

# Examples

```use statrs::distribution::Cauchy;

let n = Cauchy::new(0.0, 1.0).unwrap();
assert_eq!(n.scale(), 1.0);```

## Trait Implementations

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

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

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

# Formula

`(1 / π) * arctan((x - x_0) / γ) + 0.5`

where `x_0` is the location and `γ` is the scale

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

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

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

# Formula

`1 / (πγ * (1 + ((x - x_0) / γ)^2))`

where `x_0` is the location and `γ` is the scale

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

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

# Formula

`ln(1 / (πγ * (1 + ((x - x_0) / γ)^2)))`

where `x_0` is the location and `γ` is the scale

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

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

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

# Formula

`NEG_INF`

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

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

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

# Formula

`INF`

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

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

Returns the entropy of the cauchy distribution

# Formula

`ln(γ) + ln(4π)`

where `γ` is the scale

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

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

Returns the median of the cauchy distribution

# Formula

`x_0`

where `x_0` is the location

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

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

Returns the mode of the cauchy distribution

# Formula

`x_0`

where `x_0` is the location

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

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

Performs copy-assignment from `source`. Read more

### `impl Distribution<f64> for Cauchy`[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.