rand_distr

Struct Cauchy

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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.

Cauchy distribution

§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§

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impl<F> Cauchy<F>

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pub fn new(median: F, scale: F) -> Result<Cauchy<F>, Error>

Construct a new Cauchy with the given shape parameters median the peak location and scale the scale factor.

Trait Implementations§

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impl<F> Clone for Cauchy<F>

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fn clone(&self) -> Cauchy<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 Cauchy<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 Cauchy<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 Cauchy<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 Cauchy<F>

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fn eq(&self, other: &Cauchy<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 Cauchy<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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impl<F> Copy for Cauchy<F>

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impl<F> StructuralPartialEq for Cauchy<F>

Auto Trait Implementations§

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

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

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

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

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

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impl<F> UnwindSafe for Cauchy<F>
where F: UnwindSafe,

Blanket Implementations§

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impl<T> Any for T
where 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 T
where 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 T
where 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 T
where 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 T
where 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 T
where 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 T
where 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 T
where 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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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> DeserializeOwned for T
where T: for<'de> Deserialize<'de>,