Add distribution plots to rand_distr documentation

rand_distr/src/gumbel.rs

@@ -6,29 +6,29 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-//! The Gumbel distribution `Gumbel(μ, σ)`.
+//! The Gumbel distribution `Gumbel(μ, β)`.
 
 use crate::{Distribution, OpenClosed01};
 use core::fmt;
 use num_traits::Float;
 use rand::Rng;
 
-/// The Gumbel distribution `Gumbel(μ, σ)`.
+/// The Gumbel distribution `Gumbel(μ, β)`.
 ///
 /// The Gumbel distribution is a continuous probability distribution
-/// with location parameter `μ` and scale parameter `σ`.
+/// with location parameter `μ` (`mu`) and scale parameter `β` (`beta`).
 /// It is used to model the distribution of the maximum (or minimum)
 /// of a number of samples of various distributions.
 /// 
 /// # Density function
 ///
-/// `f(x) = exp(-(z + exp(-z))) / σ`, where `z = (x - μ) / σ`.
+/// `f(x) = exp(-(z + exp(-z))) / β`, where `z = (x - μ) / β`.
 ///
 /// # Plot
 ///
-/// The following plot illustrates the Gumbel distribution with various values of `μ` and `σ`.
+/// The following plot illustrates the Gumbel distribution with various values of `μ` and `β`.
 /// Note how the location parameter `μ` shifts the distribution along the x-axis,
-/// and the scale parameter `σ` changes the density around `μ`.
+/// and the scale parameter `β` changes the density around `μ`.
 /// Note also the asymptotic behavior of the distribution towards the right.
 ///
 /// ![Gumbel distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/gumbel.svg)

rand_distr/src/pareto.rs

@@ -6,24 +6,24 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-//! The Pareto distribution.
+//! The Pareto distribution `Pareto(α, xₘ)`.
 
 use crate::{Distribution, OpenClosed01};
 use core::fmt;
 use num_traits::Float;
 use rand::Rng;
 
-/// The Pareto distribution `Pareto(scale, shape)`.
+/// The Pareto distribution `Pareto(α, xₘ)`.
 ///
 /// The Pareto distribution is a continuous probability distribution with
-/// parameters `scale` (`α`) and `shape` (`x`<sub>`m`</sub> or `k`).
+/// parameters `scale` (`α`) and `shape` (`xₘ` or `k`).
 ///
 /// # Plot
 ///
 /// The following plot shows the Pareto distribution with various values of
 /// `scale` and `shape`.
 /// Note how the scale parameter `α` corresponds to the height of the jump
-/// in density at `x = x`<sub>`m`</sub>, and to the rate of decay in the tail.
+/// in density at `x = xₘ`, and to the rate of decay in the tail.
 ///
 /// ![Pareto distribution](https://raw.githubusercontent.com/rust-random/charts/main/charts/pareto.svg)
 ///

rand_distr/src/poisson.rs

@@ -7,17 +7,17 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-//! The Poisson distribution.
+//! The Poisson distribution `Poisson(λ)`.
 
 use crate::{Cauchy, Distribution, Standard};
 use core::fmt;
 use num_traits::{Float, FloatConst};
 use rand::Rng;
 
-/// The Poisson distribution `Poisson(lambda)`.
+/// The Poisson distribution `Poisson(λ)`.
 ///
 /// The Poisson distribution is a discrete probability distribution with
-/// rate parameter `λ`. It models the number of events occurring in a fixed
+/// rate parameter `λ` (lambda). It models the number of events occurring in a fixed
 /// interval of time or space.
 ///
 /// This distribution has density function:

rand_distr/src/skew_normal.rs

@@ -6,21 +6,25 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-//! The Skew Normal distribution.
+//! The Skew Normal distribution `SN(ξ, ω, α)`.
 
 use crate::{Distribution, StandardNormal};
 use core::fmt;
 use num_traits::Float;
 use rand::Rng;
 
-/// The [skew normal distribution] `SN(location, scale, shape)`.
+/// The [skew normal distribution] `SN(ξ, ω, α)`.
 ///
 /// The skew normal distribution is a generalization of the
 /// [`Normal`](crate::Normal) distribution to allow for non-zero skewness.
+/// It has parameters `location` (`ξ`, zeta), `scale` (`ω`, omega), and
+/// `shape` (`α`, alpha).
 ///
-/// The `location` and `scale` parameters correspond to the
-/// mean and standard deviation of the normal distribution,
-/// respectively. The `shape` parameter controls the skewness.
+/// The `ξ` and `ω` parameters correspond to the mean `μ` and standard
+/// deviation `σ` of the normal distribution, respectively.
+/// The `α` parameter controls the skewness.
+/// 
+/// # Density function
 ///
 /// It has the density function, for `scale > 0`,
 /// `f(x) = 2 / scale * phi((x - location) / scale) * Phi(alpha * (x - location) / scale)`

rand_distr/src/weibull.rs

@@ -6,15 +6,17 @@
 // option. This file may not be copied, modified, or distributed
 // except according to those terms.
 
-//! The Weibull distribution.
+//! The Weibull distribution `Weibull(λ, k)`
 
 use crate::{Distribution, OpenClosed01};
 use core::fmt;
 use num_traits::Float;
 use rand::Rng;
 
-/// Samples floating-point numbers according to the Weibull distribution.
-/// The Weibull distribution has two parameters, `scale` (`λ`) and `shape` (`k`).
+/// The Weibull distribution `Weibull(λ, k)`.
+/// This is a family of continuous probability distributions with parameters
+/// `scale` (`λ`, lambda) and `shape` (`k`). It is used to model reliability
+/// data, life data, and accelerated life testing data.
 ///
 /// # Plot
 ///

rand_distr/src/zipf.rs

@@ -15,12 +15,15 @@ use rand::{distributions::OpenClosed01, Rng};
 
 /// The Zeta distribution `Zeta(a)`.
 ///
-/// The Zeta distribution is a discrete probability distribution with parameter
-/// `a`. It is a special case of the [`Zipf`] distribution with `n = ∞`.
+/// The [Zeta distribution](https://en.wikipedia.org/wiki/Zeta_distribution)
+/// is a discrete probability distribution with parameter `a`.
+/// 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.
 ///
-/// It has the density function `f(k) = k^(-a) / C(a)` for `k >= 1`, where `a`
-/// is the parameter and `C(a)` is the Riemann zeta function.
+/// # Density function
+/// 
+/// `f(k) = k^(-a) / ζ(a)` for `k >= 1`, where `ζ` is the
+/// [Riemann zeta function](https://en.wikipedia.org/wiki/Riemann_zeta_function).
 ///
 /// # Plot
 ///
@@ -37,7 +40,7 @@ use rand::{distributions::OpenClosed01, Rng};
 /// println!("{}", val);
 /// ```
 ///
-/// # Remarks
+/// # 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
@@ -47,11 +50,9 @@ use rand::{distributions::OpenClosed01, Rng};
 ///
 /// # Implementation details
 ///
-/// We are using the algorithm from [Non-Uniform Random Variate Generation],
+/// We are using the algorithm from 
+/// [Non-Uniform Random Variate Generation](https://doi.org/10.1007/978-1-4613-8643-8),
 /// Section 6.1, page 551.
-///
-/// [zeta distribution]: https://en.wikipedia.org/wiki/Zeta_distribution
-/// [Non-Uniform Random Variate Generation]: https://doi.org/10.1007/978-1-4613-8643-8
 #[derive(Clone, Copy, Debug, PartialEq)]
 pub struct Zeta<F>
 where
@@ -131,13 +132,13 @@ where
     }
 }
 
-/// Samples integers according to the Zipf distribution.
+/// The Zipf distribution `Zipf(n, s)`.
 ///
 /// The samples follow Zipf's law: The frequency of each sample from a finite
 /// set of size `n` is inversely proportional to a power of its frequency rank
 /// (with exponent `s`).
 ///
-/// For large `n`, this converges to the [`Zeta`] distribution.
+/// For large `n`, this converges to the [`Zeta`](crate::Zeta) distribution.
 ///
 /// For `s = 0`, this becomes a uniform distribution.
 ///