Struct rand_distr::Zeta

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

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;

let val: f64 = thread_rng().sample(Zeta::new(1.5).unwrap());
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

impl<F> Zeta<F>

where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

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

Construct a new Zeta distribution with given s parameter.

Trait Implementations

impl<F> Clone for Zeta<F>

where F: Float + Clone, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

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

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl<F> Debug for Zeta<F>

where F: Float + Debug, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl<F> Distribution<F> for Zeta<F>

where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> F

Generate a random value of T, using rng as the source of randomness.

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.

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

impl<F> PartialEq for Zeta<F>

where F: Float + PartialEq, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

fn eq(&self, other: &Zeta<F>) -> bool

Tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl<F> Copy for Zeta<F>

where F: Float + Copy, Standard: Distribution<F>, OpenClosed01: Distribution<F>,

impl<F> StructuralPartialEq for Zeta<F>

where F: Float, Standard: Distribution<F>, OpenClosed01: Distribution<F>,