# Struct rand_distr::Zeta

``````pub struct Zeta<F>where
F: Float,
Standard: Distribution<F>,
OpenClosed01: Distribution<F>,{ /* private fields */ }``````
Expand description

The Zeta distribution `Zeta(s)`.

The Zeta distribution is a discrete probability distribution with parameter `s`. It is a special case of the `Zipf` distribution with `n = ∞`. It is also known as the discrete Pareto, Riemann-Zeta, Zipf, or Zipf–Estoup distribution.

## §Density function

`f(k) = k^(-s) / ζ(s)` for `k >= 1`, where `ζ` is the Riemann zeta function.

## §Plot

The following plot illustrates the zeta distribution for various values of `s`.

## §Example

``````use rand::prelude::*;
use rand_distr::Zeta;

println!("{}", val);``````

## §Notes

The zeta distribution has no upper limit. Sampled values may be infinite. In particular, a value of infinity might be returned for the following reasons:

1. it is the best representation in the type `F` of the actual sample.
2. to prevent infinite loops for very small `s`.

## §Implementation details

We are using the algorithm from Non-Uniform Random Variate Generation, Section 6.1, page 551.

## Implementations§

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### impl<F> Zeta<F>where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

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#### pub fn new(s: F) -> Result<Zeta<F>, Error>

Construct a new `Zeta` distribution with given `s` parameter.

## Trait Implementations§

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### impl<F> Clone for Zeta<F>where F: Float + Clone, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

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#### fn clone(&self) -> Zeta<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 Zeta<F>where F: Float + Debug, Standard: Distribution<F>, OpenClosed01: Distribution<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<F> Distribution<F> for Zeta<F>where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<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 Zeta<F>where F: Float + PartialEq, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

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#### fn eq(&self, other: &Zeta<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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## Blanket Implementations§

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### impl<T> Any for Twhere 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 Twhere 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 Twhere 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 Twhere 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 Twhere 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 Twhere 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 Twhere 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 Twhere 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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