`pub struct Cauchy<F>{ /* private fields */ }`

## Expand description

The Cauchy distribution `Cauchy(x₀, γ)`

.

The Cauchy distribution is a continuous probability distribution with
parameters `x₀`

(median) and `γ`

(scale).
It describes the distribution of the ratio of two independent
normally distributed random variables with means `x₀`

and scales `γ`

.
In other words, if `X`

and `Y`

are independent normally distributed
random variables with means `x₀`

and scales `γ`

, respectively, then
`X / Y`

is `Cauchy(x₀, γ)`

distributed.

## §Density function

`f(x) = 1 / (π * γ * (1 + ((x - x₀) / γ)²))`

## §Plot

The plot illustrates the Cauchy distribution with various values of `x₀`

and `γ`

.
Note how the median parameter `x₀`

shifts the distribution along the x-axis,
and how the scale `γ`

changes the density around the median.

The standard Cauchy distribution is the special case with `x₀ = 0`

and `γ = 1`

,
which corresponds to the ratio of two `StandardNormal`

distributions.

## §Example

```
use rand_distr::{Cauchy, Distribution};
let cau = Cauchy::new(2.0, 5.0).unwrap();
let v = cau.sample(&mut rand::rng());
println!("{} is from a Cauchy(2, 5) distribution", v);
```

## §Notes

Note that at least for `f32`

, results are not fully portable due to minor
differences in the target system’s *tan* implementation, `tanf`

.

## Implementations§

## Trait Implementations§

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

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

### impl<F> Distribution<F> for Cauchy<F>

### impl<F> Copy for Cauchy<F>

### impl<F> StructuralPartialEq for Cauchy<F>

## Auto Trait Implementations§

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

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

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

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

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

### impl<F> UnwindSafe for Cauchy<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`

)