From 3844e92a3265852548ca05ac9e8c71447108f414 Mon Sep 17 00:00:00 2001
From: Orion Yeung <11580988+orionyeung001@users.noreply.github.com>
Date: Tue, 5 Nov 2024 10:43:19 -0600
Subject: [PATCH] doc: updates doc tests to use new traits

---
 src/distribution/bernoulli.rs               | 19 +++++++++-------
 src/distribution/beta.rs                    | 17 +++++++++------
 src/distribution/binomial.rs                | 19 +++++++++-------
 src/distribution/categorical.rs             |  9 ++++----
 src/distribution/cauchy.rs                  | 17 +++++++++------
 src/distribution/chi.rs                     | 13 ++++++-----
 src/distribution/chi_squared.rs             | 24 ++++++++++++---------
 src/distribution/dirac.rs                   |  9 ++++----
 src/distribution/dirichlet.rs               | 15 +++++++------
 src/distribution/discrete_uniform.rs        | 14 ++++++++----
 src/distribution/empirical.rs               |  2 +-
 src/distribution/erlang.rs                  | 17 +++++++++------
 src/distribution/exponential.rs             | 15 +++++++------
 src/distribution/fisher_snedecor.rs         | 15 +++++++------
 src/distribution/gamma.rs                   | 17 +++++++++------
 src/distribution/geometric.rs               | 13 ++++++-----
 src/distribution/gumbel.rs                  | 23 +++++++++++++-------
 src/distribution/hypergeometric.rs          |  8 +++----
 src/distribution/inverse_gamma.rs           |  6 +++---
 src/distribution/log_normal.rs              |  8 +++----
 src/distribution/multinomial.rs             |  4 ++--
 src/distribution/multivariate_normal.rs     |  6 +++---
 src/distribution/multivariate_students_t.rs |  6 +++---
 src/distribution/negative_binomial.rs       | 10 ++++-----
 src/distribution/normal.rs                  |  7 +++---
 src/distribution/pareto.rs                  | 14 +++++-------
 src/distribution/poisson.rs                 |  8 +++----
 src/distribution/students_t.rs              |  8 +++----
 src/distribution/triangular.rs              |  4 ++--
 src/distribution/uniform.rs                 |  4 ++--
 src/distribution/weibull.rs                 |  9 ++++----
 src/lib.rs                                  | 12 +++++------
 32 files changed, 209 insertions(+), 163 deletions(-)

diff --git a/src/distribution/bernoulli.rs b/src/distribution/bernoulli.rs
index 066c15c2..c4b413c6 100644
--- a/src/distribution/bernoulli.rs
+++ b/src/distribution/bernoulli.rs
@@ -10,13 +10,14 @@ use crate::statistics::*;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Bernoulli, Discrete};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Bernoulli, BinomialError, Discrete};
+/// use statrs::statistics::*;
 ///
-/// let n = Bernoulli::new(0.5).unwrap();
-/// assert_eq!(n.mean().unwrap(), 0.5);
+/// let n = Bernoulli::new(0.5)?;
+/// assert_eq!(n.mean(), 0.5);
 /// assert_eq!(n.pmf(0), 0.5);
 /// assert_eq!(n.pmf(1), 0.5);
+/// # Ok::<(), BinomialError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Bernoulli {
@@ -53,10 +54,11 @@ impl Bernoulli {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Bernoulli;
+    /// use statrs::distribution::{Bernoulli, BinomialError};
     ///
-    /// let n = Bernoulli::new(0.5).unwrap();
+    /// let n = Bernoulli::new(0.5)?;
     /// assert_eq!(n.p(), 0.5);
+    /// # Ok::<(), BinomialError>(())
     /// ```
     pub fn p(&self) -> f64 {
         self.b.p()
@@ -68,10 +70,11 @@ impl Bernoulli {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Bernoulli;
+    /// use statrs::distribution::{Bernoulli, BinomialError};
     ///
-    /// let n = Bernoulli::new(0.5).unwrap();
+    /// let n = Bernoulli::new(0.5)?;
     /// assert_eq!(n.n(), 1);
+    /// # Ok::<(), BinomialError>(())
     /// ```
     pub fn n(&self) -> u64 {
         1
diff --git a/src/distribution/beta.rs b/src/distribution/beta.rs
index b00be4a3..dd0d1cee 100644
--- a/src/distribution/beta.rs
+++ b/src/distribution/beta.rs
@@ -8,13 +8,14 @@ use crate::statistics::*;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Beta, Continuous};
+/// use statrs::distribution::{Beta, Continuous, BetaError};
 /// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = Beta::new(2.0, 2.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 0.5);
+/// let n = Beta::new(2.0, 2.0)?;
+/// assert_eq!(n.mean(), 0.5);
 /// assert!(prec::almost_eq(n.pdf(0.5), 1.5, 1e-14));
+/// # Ok::<(), BetaError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Beta {
@@ -82,10 +83,11 @@ impl Beta {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Beta;
+    /// use statrs::distribution::{Beta, BetaError};
     ///
-    /// let n = Beta::new(1.0, 2.0).unwrap();
+    /// let n = Beta::new(1.0, 2.0)?;
     /// assert_eq!(n.shape_a(), 1.0);
+    /// # Ok::<(), BetaError>(())
     /// ```
     pub fn shape_a(&self) -> f64 {
         self.shape_a
@@ -96,10 +98,11 @@ impl Beta {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Beta;
+    /// use statrs::distribution::{Beta, BetaError};
     ///
-    /// let n = Beta::new(1.0, 2.0).unwrap();
+    /// let n = Beta::new(1.0, 2.0)?;
     /// assert_eq!(n.shape_b(), 2.0);
+    /// # Ok::<(), BetaError>(())
     /// ```
     pub fn shape_b(&self) -> f64 {
         self.shape_b
diff --git a/src/distribution/binomial.rs b/src/distribution/binomial.rs
index f441e2b9..4b8a3d66 100644
--- a/src/distribution/binomial.rs
+++ b/src/distribution/binomial.rs
@@ -10,13 +10,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Binomial, Discrete};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Binomial, BinomialError, Discrete};
+/// use statrs::statistics::*;
 ///
-/// let n = Binomial::new(0.5, 5).unwrap();
-/// assert_eq!(n.mean().unwrap(), 2.5);
+/// let n = Binomial::new(0.5, 5)?;
+/// assert_eq!(n.mean(), 2.5);
 /// assert_eq!(n.pmf(0), 0.03125);
 /// assert_eq!(n.pmf(3), 0.3125);
+/// # Ok::<(), BinomialError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Binomial {
@@ -78,10 +79,11 @@ impl Binomial {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Binomial;
+    /// use statrs::distribution::{Binomial, BinomialError};
     ///
-    /// let n = Binomial::new(0.5, 5).unwrap();
+    /// let n = Binomial::new(0.5, 5)?;
     /// assert_eq!(n.p(), 0.5);
+    /// # Ok::<(), BinomialError>(())
     /// ```
     pub fn p(&self) -> f64 {
         self.p
@@ -93,10 +95,11 @@ impl Binomial {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Binomial;
+    /// use statrs::distribution::{Binomial, BinomialError};
     ///
-    /// let n = Binomial::new(0.5, 5).unwrap();
+    /// let n = Binomial::new(0.5, 5)?;
     /// assert_eq!(n.n(), 5);
+    /// # Ok::<(), BinomialError>(())
     /// ```
     pub fn n(&self) -> u64 {
         self.n
diff --git a/src/distribution/categorical.rs b/src/distribution/categorical.rs
index e46d0faa..e26cf626 100644
--- a/src/distribution/categorical.rs
+++ b/src/distribution/categorical.rs
@@ -10,13 +10,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Categorical, Discrete};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Categorical, CategoricalError, Discrete};
+/// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = Categorical::new(&[0.0, 1.0, 2.0]).unwrap();
-/// assert!(prec::almost_eq(n.mean().unwrap(), 5.0 / 3.0, 1e-15));
+/// let n = Categorical::new(&[0.0, 1.0, 2.0])?;
+/// assert!(prec::almost_eq(n.mean(), 5.0 / 3.0, 1e-15));
 /// assert_eq!(n.pmf(1), 1.0 / 3.0);
+/// # Ok::<(), CategoricalError>(())
 /// ```
 #[derive(Clone, PartialEq, Debug)]
 pub struct Categorical {
diff --git a/src/distribution/cauchy.rs b/src/distribution/cauchy.rs
index 0e2d6768..32e5b37d 100644
--- a/src/distribution/cauchy.rs
+++ b/src/distribution/cauchy.rs
@@ -8,12 +8,13 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Cauchy, Continuous};
-/// use statrs::statistics::Mode;
+/// use statrs::distribution::{Cauchy, Continuous, CauchyError};
+/// use statrs::statistics::*;
 ///
-/// let n = Cauchy::new(0.0, 1.0).unwrap();
+/// let n = Cauchy::new(0.0, 1.0)?;
 /// assert_eq!(n.mode().unwrap(), 0.0);
 /// assert_eq!(n.pdf(1.0), 0.1591549430918953357689);
+/// # Ok::<(), CauchyError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Cauchy {
@@ -80,10 +81,11 @@ impl Cauchy {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Cauchy;
+    /// use statrs::distribution::{Cauchy, CauchyError};
     ///
-    /// let n = Cauchy::new(0.0, 1.0).unwrap();
+    /// let n = Cauchy::new(0.0, 1.0)?;
     /// assert_eq!(n.location(), 0.0);
+    /// # Ok::<(), CauchyError>(())
     /// ```
     pub fn location(&self) -> f64 {
         self.location
@@ -94,10 +96,11 @@ impl Cauchy {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Cauchy;
+    /// use statrs::distribution::{Cauchy, CauchyError};
     ///
-    /// let n = Cauchy::new(0.0, 1.0).unwrap();
+    /// let n = Cauchy::new(0.0, 1.0)?;
     /// assert_eq!(n.scale(), 1.0);
+    /// # Ok::<(), CauchyError>(())
     /// ```
     pub fn scale(&self) -> f64 {
         self.scale
diff --git a/src/distribution/chi.rs b/src/distribution/chi.rs
index 072c2356..75729b3e 100644
--- a/src/distribution/chi.rs
+++ b/src/distribution/chi.rs
@@ -9,13 +9,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Chi, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Chi, Continuous, ChiError};
+/// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = Chi::new(2.0).unwrap();
+/// let n = Chi::new(2.0)?;
 /// assert!(prec::almost_eq(n.mean().unwrap(), 1.25331413731550025121, 1e-14));
 /// assert!(prec::almost_eq(n.pdf(1.0), 0.60653065971263342360, 1e-15));
+/// # Ok::<(), ChiError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Chi {
@@ -77,10 +78,12 @@ impl Chi {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Chi;
+    /// use statrs::distribution::{Chi, ChiError};
+    ///
     ///
-    /// let n = Chi::new(2.0).unwrap();
+    /// let n = Chi::new(2.0)?;
     /// assert_eq!(n.freedom(), 2.0);
+    /// # Ok::<(), ChiError>(())
     /// ```
     pub fn freedom(&self) -> f64 {
         self.freedom
diff --git a/src/distribution/chi_squared.rs b/src/distribution/chi_squared.rs
index 524df2b5..d0cb939d 100644
--- a/src/distribution/chi_squared.rs
+++ b/src/distribution/chi_squared.rs
@@ -11,13 +11,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{ChiSquared, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{ChiSquared, Continuous, GammaError};
+/// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = ChiSquared::new(3.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 3.0);
+/// let n = ChiSquared::new(3.0)?;
+/// assert_eq!(n.mean(), 3.0);
 /// assert!(prec::almost_eq(n.pdf(4.0), 0.107981933026376103901, 1e-15));
+/// # Ok::<(), GammaError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct ChiSquared {
@@ -56,10 +57,11 @@ impl ChiSquared {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::ChiSquared;
+    /// use statrs::distribution::{ChiSquared, GammaError};
     ///
-    /// let n = ChiSquared::new(3.0).unwrap();
+    /// let n = ChiSquared::new(3.0)?;
     /// assert_eq!(n.freedom(), 3.0);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn freedom(&self) -> f64 {
         self.freedom
@@ -70,10 +72,11 @@ impl ChiSquared {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::ChiSquared;
+    /// use statrs::distribution::{ChiSquared, GammaError};
     ///
-    /// let n = ChiSquared::new(3.0).unwrap();
+    /// let n = ChiSquared::new(3.0)?;
     /// assert_eq!(n.shape(), 3.0 / 2.0);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn shape(&self) -> f64 {
         self.g.shape()
@@ -84,10 +87,11 @@ impl ChiSquared {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::ChiSquared;
+    /// use statrs::distribution::{ChiSquared, GammaError};
     ///
-    /// let n = ChiSquared::new(3.0).unwrap();
+    /// let n = ChiSquared::new(3.0)?;
     /// assert_eq!(n.rate(), 0.5);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn rate(&self) -> f64 {
         self.g.rate()
diff --git a/src/distribution/dirac.rs b/src/distribution/dirac.rs
index 0420cdf1..056213b4 100644
--- a/src/distribution/dirac.rs
+++ b/src/distribution/dirac.rs
@@ -7,11 +7,12 @@ use crate::statistics::*;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Dirac, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Dirac, Continuous, DiracError};
+/// use statrs::statistics::*;
 ///
-/// let n = Dirac::new(3.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 3.0);
+/// let n = Dirac::new(3.0)?;
+/// assert_eq!(n.mean(), 3.0);
+/// # Ok::<(), DiracError>(())
 /// ```
 #[derive(Debug, Copy, Clone, PartialEq)]
 pub struct Dirac(f64);
diff --git a/src/distribution/dirichlet.rs b/src/distribution/dirichlet.rs
index 5e902b63..69a424ef 100644
--- a/src/distribution/dirichlet.rs
+++ b/src/distribution/dirichlet.rs
@@ -12,14 +12,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Dirichlet, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Dirichlet, Continuous, DirichletError};
+/// use statrs::statistics::*;
 /// use nalgebra::DVector;
-/// use statrs::statistics::MeanN;
 ///
-/// let n = Dirichlet::new(vec![1.0, 2.0, 3.0]).unwrap();
-/// assert_eq!(n.mean().unwrap(), DVector::from_vec(vec![1.0 / 6.0, 1.0 / 3.0, 0.5]));
+/// let n = Dirichlet::new(vec![1.0, 2.0, 3.0])?;
+/// assert_eq!(n.mean(), DVector::from_vec(vec![1.0 / 6.0, 1.0 / 3.0, 0.5]));
 /// assert_eq!(n.pdf(&DVector::from_vec(vec![0.33333, 0.33333, 0.33333])), 2.222155556222205);
+/// # Ok::<(), DirichletError>(())
 /// ```
 #[derive(Clone, PartialEq, Debug)]
 pub struct Dirichlet<D>
@@ -138,11 +138,12 @@ where
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Dirichlet;
+    /// use statrs::distribution::{Dirichlet, DirichletError};
     /// use nalgebra::DVector;
     ///
-    /// let n = Dirichlet::new(vec![1.0, 2.0, 3.0]).unwrap();
+    /// let n = Dirichlet::new(vec![1.0, 2.0, 3.0])?;
     /// assert_eq!(n.alpha(), &DVector::from_vec(vec![1.0, 2.0, 3.0]));
+    /// # Ok::<(), DirichletError>(())
     /// ```
     pub fn alpha(&self) -> &nalgebra::OVector<f64, D> {
         &self.alpha
diff --git a/src/distribution/discrete_uniform.rs b/src/distribution/discrete_uniform.rs
index 447c15a3..382c5104 100644
--- a/src/distribution/discrete_uniform.rs
+++ b/src/distribution/discrete_uniform.rs
@@ -8,12 +8,13 @@ use crate::statistics::*;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{DiscreteUniform, Discrete};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{DiscreteUniform, Discrete, DiscreteUniformError};
+/// use statrs::statistics::*;
 ///
-/// let n = DiscreteUniform::new(0, 5).unwrap();
-/// assert_eq!(n.mean().unwrap(), 2.5);
+/// let n = DiscreteUniform::new(0, 5)?;
+/// assert_eq!(n.mean(), 2.5);
 /// assert_eq!(n.pmf(3), 1.0 / 6.0);
+/// # Ok::<(), DiscreteUniformError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct DiscreteUniform {
@@ -66,6 +67,11 @@ impl DiscreteUniform {
             Ok(DiscreteUniform { min, max })
         }
     }
+
+    pub fn std_dev(&self) -> f64 {
+        let dist = self.max - self.min + 1;
+        (dist * dist) as f64 / 12.
+    }
 }
 
 impl std::fmt::Display for DiscreteUniform {
diff --git a/src/distribution/empirical.rs b/src/distribution/empirical.rs
index 88805120..9545e637 100644
--- a/src/distribution/empirical.rs
+++ b/src/distribution/empirical.rs
@@ -27,7 +27,7 @@ impl<T: PartialOrd> Ord for NonNan<T> {
 ///
 /// ```
 /// use statrs::distribution::{Continuous, Empirical};
-/// use statrs::statistics::Distribution;
+/// use statrs::statistics::*;
 ///
 /// let samples = vec![0.0, 5.0, 10.0];
 ///
diff --git a/src/distribution/erlang.rs b/src/distribution/erlang.rs
index 333800aa..97d1b264 100644
--- a/src/distribution/erlang.rs
+++ b/src/distribution/erlang.rs
@@ -10,13 +10,14 @@ use crate::statistics::*;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Erlang, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Erlang, Continuous, GammaError};
+/// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = Erlang::new(3, 1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 3.0);
+/// let n = Erlang::new(3, 1.0)?;
+/// assert_eq!(n.mean(), 3.0);
 /// assert!(prec::almost_eq(n.pdf(2.0), 0.270670566473225383788, 1e-15));
+/// # Ok::<(), GammaError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Erlang {
@@ -52,10 +53,11 @@ impl Erlang {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Erlang;
+    /// use statrs::distribution::{Erlang, GammaError};
     ///
-    /// let n = Erlang::new(3, 1.0).unwrap();
+    /// let n = Erlang::new(3, 1.0)?;
     /// assert_eq!(n.shape(), 3);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn shape(&self) -> u64 {
         self.g.shape() as u64
@@ -66,10 +68,11 @@ impl Erlang {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Erlang;
+    /// use statrs::distribution::{Erlang, GammaError};
     ///
     /// let n = Erlang::new(3, 1.0).unwrap();
     /// assert_eq!(n.rate(), 1.0);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn rate(&self) -> f64 {
         self.g.rate()
diff --git a/src/distribution/exponential.rs b/src/distribution/exponential.rs
index 28274662..18364a93 100644
--- a/src/distribution/exponential.rs
+++ b/src/distribution/exponential.rs
@@ -11,13 +11,15 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Exp, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Exp, Continuous, ExpError};
+/// use statrs::statistics::*;
 ///
-/// let n = Exp::new(1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 1.0);
+/// let n = Exp::new(1.0)?;
+/// assert_eq!(n.mean(), 1.0);
 /// assert_eq!(n.pdf(1.0), 0.3678794411714423215955);
+/// # Ok::<(), ExpError>(())
 /// ```
+#[doc(alias = "Exponential")]
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Exp {
     rate: f64,
@@ -74,10 +76,11 @@ impl Exp {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Exp;
+    /// use statrs::distribution::{Exp, ExpError};
     ///
-    /// let n = Exp::new(1.0).unwrap();
+    /// let n = Exp::new(1.0)?;
     /// assert_eq!(n.rate(), 1.0);
+    /// # Ok::<(), ExpError>(())
     /// ```
     pub fn rate(&self) -> f64 {
         self.rate
diff --git a/src/distribution/fisher_snedecor.rs b/src/distribution/fisher_snedecor.rs
index ded4f654..12d1c3ca 100644
--- a/src/distribution/fisher_snedecor.rs
+++ b/src/distribution/fisher_snedecor.rs
@@ -10,13 +10,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{FisherSnedecor, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{FisherSnedecor, Continuous, FisherSnedecorError};
+/// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = FisherSnedecor::new(3.0, 3.0).unwrap();
+/// let n = FisherSnedecor::new(3.0, 3.0)?;
 /// assert_eq!(n.mean().unwrap(), 3.0);
 /// assert!(prec::almost_eq(n.pdf(1.0), 0.318309886183790671538, 1e-15));
+/// # Ok::<(), FisherSnedecorError>(())
 /// ```
 #[derive(Debug, Copy, Clone, PartialEq)]
 pub struct FisherSnedecor {
@@ -92,10 +93,11 @@ impl FisherSnedecor {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::FisherSnedecor;
+    /// use statrs::distribution::{FisherSnedecor, FisherSnedecorError};
     ///
-    /// let n = FisherSnedecor::new(2.0, 3.0).unwrap();
+    /// let n = FisherSnedecor::new(2.0, 3.0)?;
     /// assert_eq!(n.freedom_1(), 2.0);
+    /// # Ok::<(), FisherSnedecorError>(())
     /// ```
     pub fn freedom_1(&self) -> f64 {
         self.freedom_1
@@ -107,10 +109,11 @@ impl FisherSnedecor {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::FisherSnedecor;
+    /// use statrs::distribution::{FisherSnedecor, FisherSnedecorError};
     ///
     /// let n = FisherSnedecor::new(2.0, 3.0).unwrap();
     /// assert_eq!(n.freedom_2(), 3.0);
+    /// # Ok::<(), FisherSnedecorError>(())
     /// ```
     pub fn freedom_2(&self) -> f64 {
         self.freedom_2
diff --git a/src/distribution/gamma.rs b/src/distribution/gamma.rs
index 190d4034..7542b1ec 100644
--- a/src/distribution/gamma.rs
+++ b/src/distribution/gamma.rs
@@ -9,13 +9,14 @@ use crate::statistics::*;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Gamma, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Gamma, Continuous, GammaError};
+/// use statrs::statistics::*;
 /// use statrs::prec;
 ///
-/// let n = Gamma::new(3.0, 1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 3.0);
+/// let n = Gamma::new(3.0, 1.0)?;
+/// assert_eq!(n.mean(), 3.0);
 /// assert!(prec::almost_eq(n.pdf(2.0), 0.270670566473225383788, 1e-15));
+/// # Ok::<(), GammaError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Gamma {
@@ -91,10 +92,11 @@ impl Gamma {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Gamma;
+    /// use statrs::distribution::{Gamma, GammaError};
     ///
-    /// let n = Gamma::new(3.0, 1.0).unwrap();
+    /// let n = Gamma::new(3.0, 1.0)?;
     /// assert_eq!(n.shape(), 3.0);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn shape(&self) -> f64 {
         self.shape
@@ -105,10 +107,11 @@ impl Gamma {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Gamma;
+    /// use statrs::distribution::{Gamma, GammaError};
     ///
     /// let n = Gamma::new(3.0, 1.0).unwrap();
     /// assert_eq!(n.rate(), 1.0);
+    /// # Ok::<(), GammaError>(())
     /// ```
     pub fn rate(&self) -> f64 {
         self.rate
diff --git a/src/distribution/geometric.rs b/src/distribution/geometric.rs
index 995fa5ff..e1477101 100644
--- a/src/distribution/geometric.rs
+++ b/src/distribution/geometric.rs
@@ -9,13 +9,14 @@ use std::f64;
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Geometric, Discrete};
-/// use statrs::statistics::Distribution;
+/// use statrs::distribution::{Geometric, GeometricError, Discrete};
+/// use statrs::statistics::*;
 ///
-/// let n = Geometric::new(0.3).unwrap();
-/// assert_eq!(n.mean().unwrap(), 1.0 / 0.3);
+/// let n = Geometric::new(0.3)?;
+/// assert_eq!(n.mean(), 1.0 / 0.3);
 /// assert_eq!(n.pmf(1), 0.3);
 /// assert_eq!(n.pmf(2), 0.21);
+/// # Ok::<(), GeometricError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Geometric {
@@ -75,9 +76,11 @@ impl Geometric {
     ///
     /// ```
     /// use statrs::distribution::Geometric;
+    /// # use statrs::distribution::GeometricError;
     ///
-    /// let n = Geometric::new(0.5).unwrap();
+    /// let n = Geometric::new(0.5)?;
     /// assert_eq!(n.p(), 0.5);
+    /// # Ok::<(), GeometricError>(())
     /// ```
     pub fn p(&self) -> f64 {
         self.p
diff --git a/src/distribution/gumbel.rs b/src/distribution/gumbel.rs
index c7e9c244..42a8dc45 100644
--- a/src/distribution/gumbel.rs
+++ b/src/distribution/gumbel.rs
@@ -9,13 +9,14 @@ use std::f64::{self, consts::PI};
 /// # Examples
 ///
 /// ```
-/// use statrs::distribution::{Gumbel, Continuous};
-/// use statrs::{consts::EULER_MASCHERONI, statistics::Distribution};
+/// use statrs::distribution::{Gumbel, Continuous, GumbelError};
+/// use statrs::{consts::EULER_MASCHERONI, statistics::*};
 ///
-/// let n = Gumbel::new(0.0, 1.0).unwrap();
+/// let n = Gumbel::new(0.0, 1.0)?;
 /// assert_eq!(n.location(), 0.0);
-/// assert_eq!(n.skewness().unwrap(), 1.13955);
+/// assert_eq!(n.mean(), 0.5772156649015329);
 /// assert_eq!(n.pdf(0.0), 0.36787944117144233);
+/// # Ok::<(), GumbelError>(())
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Gumbel {
@@ -82,10 +83,11 @@ impl Gumbel {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Gumbel;
+    /// use statrs::distribution::{Gumbel, GumbelError};
     ///
-    /// let n = Gumbel::new(0.0, 1.0).unwrap();
+    /// let n = Gumbel::new(0.0, 1.0)?;
     /// assert_eq!(n.location(), 0.0);
+    /// # Ok::<(), GumbelError>(())
     /// ```
     pub fn location(&self) -> f64 {
         self.location
@@ -96,14 +98,19 @@ impl Gumbel {
     /// # Examples
     ///
     /// ```
-    /// use statrs::distribution::Gumbel;
+    /// use statrs::distribution::{Gumbel, GumbelError};
     ///
-    /// let n = Gumbel::new(0.0, 1.0).unwrap();
+    /// let n = Gumbel::new(0.0, 1.0)?;
     /// assert_eq!(n.scale(), 1.0);
+    /// # Ok::<(), GumbelError>(())
     /// ```
     pub fn scale(&self) -> f64 {
         self.scale
     }
+
+    pub fn std_dev(&self) -> f64 {
+        (PI * self.scale) / 6_f64.sqrt()
+    }
 }
 
 impl std::fmt::Display for Gumbel {
diff --git a/src/distribution/hypergeometric.rs b/src/distribution/hypergeometric.rs
index ba6d3456..409ee548 100644
--- a/src/distribution/hypergeometric.rs
+++ b/src/distribution/hypergeometric.rs
@@ -12,13 +12,13 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{Hypergeometric, Discrete};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = Hypergeometric::new(500, 50, 100).unwrap();
 /// assert_eq!(n.mean().unwrap(), 10.);
-/// assert!(prec::almost_eq(n.pmf(10), 0.14736784, 1e-8));
-/// assert!(prec::almost_eq(n.pmf(25), 3.537e-7, 1e-10));
+/// assert_relative_eq!(n.pmf(10), 0.14736784, epsilon=1e-8);
+/// assert_relative_eq!(n.pmf(25), 3.537e-7, epsilon=1e-10);
 /// ```
 #[derive(Copy, Clone, PartialEq, Eq, Debug)]
 pub struct Hypergeometric {
diff --git a/src/distribution/inverse_gamma.rs b/src/distribution/inverse_gamma.rs
index 88abf91f..0cb40da7 100644
--- a/src/distribution/inverse_gamma.rs
+++ b/src/distribution/inverse_gamma.rs
@@ -11,11 +11,11 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{InverseGamma, Continuous};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = InverseGamma::new(1.1, 0.1).unwrap();
-/// assert!(prec::almost_eq(n.mean().unwrap(), 1.0, 1e-14));
+/// assert_relative_eq!(n.mean().unwrap(), 1.0, epsilon=1e-14);
 /// assert_eq!(n.pdf(1.0), 0.07554920138253064);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
diff --git a/src/distribution/log_normal.rs b/src/distribution/log_normal.rs
index da377705..2bcb5960 100644
--- a/src/distribution/log_normal.rs
+++ b/src/distribution/log_normal.rs
@@ -12,12 +12,12 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{LogNormal, Continuous};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = LogNormal::new(0.0, 1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), (0.5f64).exp());
-/// assert!(prec::almost_eq(n.pdf(1.0), 0.3989422804014326779399, 1e-16));
+/// assert_eq!(n.mean(), (0.5f64).exp());
+/// assert_relative_eq!(n.pdf(1.0), 0.3989422804014326779399, epsilon=1e-16);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct LogNormal {
diff --git a/src/distribution/multinomial.rs b/src/distribution/multinomial.rs
index b62003c5..40532919 100644
--- a/src/distribution/multinomial.rs
+++ b/src/distribution/multinomial.rs
@@ -13,11 +13,11 @@ use nalgebra::{Cholesky, Dim, DimMin, Dyn, OMatrix, OVector};
 ///
 /// ```
 /// use statrs::distribution::Multinomial;
-/// use statrs::statistics::MeanN;
+/// use statrs::statistics::*;
 /// use nalgebra::vector;
 ///
 /// let n = Multinomial::new_from_nalgebra(vector![0.3, 0.7], 5).unwrap();
-/// assert_eq!(n.mean().unwrap(), (vector![1.5, 3.5]));
+/// assert_eq!(n.mean(), (vector![1.5, 3.5]));
 /// ```
 #[derive(Debug, Clone, PartialEq)]
 pub struct Multinomial<D>
diff --git a/src/distribution/multivariate_normal.rs b/src/distribution/multivariate_normal.rs
index 9754a96d..1c52d375 100644
--- a/src/distribution/multivariate_normal.rs
+++ b/src/distribution/multivariate_normal.rs
@@ -78,11 +78,11 @@ where
 /// ```
 /// use statrs::distribution::{MultivariateNormal, Continuous};
 /// use nalgebra::{matrix, vector};
-/// use statrs::statistics::{MeanN, VarianceN};
+/// use statrs::statistics::*;
 ///
 /// let mvn = MultivariateNormal::new_from_nalgebra(vector![0., 0.], matrix![1., 0.; 0., 1.]).unwrap();
-/// assert_eq!(mvn.mean().unwrap(), vector![0., 0.]);
-/// assert_eq!(mvn.variance().unwrap(), matrix![1., 0.; 0., 1.]);
+/// assert_eq!(mvn.mean(), vector![0., 0.]);
+/// assert_eq!(mvn.variance(), matrix![1., 0.; 0., 1.]);
 /// assert_eq!(mvn.pdf(&vector![1.,  1.]), 0.05854983152431917);
 /// ```
 #[derive(Clone, PartialEq, Debug)]
diff --git a/src/distribution/multivariate_students_t.rs b/src/distribution/multivariate_students_t.rs
index bc034397..3f169428 100644
--- a/src/distribution/multivariate_students_t.rs
+++ b/src/distribution/multivariate_students_t.rs
@@ -14,11 +14,11 @@ use std::f64::consts::PI;
 /// ```
 /// use statrs::distribution::{MultivariateStudent, Continuous};
 /// use nalgebra::{DVector, DMatrix};
-/// use statrs::statistics::{MeanN, VarianceN};
+/// use statrs::statistics::*;
 ///
 /// let mvs = MultivariateStudent::new(vec![0., 0.], vec![1., 0., 0., 1.], 4.).unwrap();
-/// assert_eq!(mvs.mean().unwrap(), DVector::from_vec(vec![0., 0.]));
-/// assert_eq!(mvs.variance().unwrap(), DMatrix::from_vec(2, 2, vec![2., 0., 0., 2.]));
+/// assert_eq!(mvs.mean(), Some(DVector::from_vec(vec![0., 0.])));
+/// assert_eq!(mvs.variance(), Some(DMatrix::from_vec(2, 2, vec![2., 0., 0., 2.])));
 /// assert_eq!(mvs.pdf(&DVector::from_vec(vec![1.,  1.])), 0.04715702017537655);
 /// ```
 #[derive(Debug, Clone, PartialEq)]
diff --git a/src/distribution/negative_binomial.rs b/src/distribution/negative_binomial.rs
index b56ff268..f42252dd 100644
--- a/src/distribution/negative_binomial.rs
+++ b/src/distribution/negative_binomial.rs
@@ -25,13 +25,13 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{NegativeBinomial, Discrete};
-/// use statrs::statistics::DiscreteDistribution;
-/// use statrs::prec::almost_eq;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let r = NegativeBinomial::new(4.0, 0.5).unwrap();
-/// assert_eq!(r.mean().unwrap(), 4.0);
-/// assert!(almost_eq(r.pmf(0), 0.0625, 1e-8));
-/// assert!(almost_eq(r.pmf(3), 0.15625, 1e-8));
+/// assert_eq!(r.mean(), 4.0);
+/// assert_relative_eq!(r.pmf(0), 0.0625, epsilon=1e-8);
+/// assert_relative_eq!(r.pmf(3), 0.15625, epsilon=1e-8);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct NegativeBinomial {
diff --git a/src/distribution/normal.rs b/src/distribution/normal.rs
index cfce032f..0407ec7f 100644
--- a/src/distribution/normal.rs
+++ b/src/distribution/normal.rs
@@ -11,11 +11,12 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{Normal, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = Normal::new(0.0, 1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 0.0);
-/// assert_eq!(n.pdf(1.0), 0.2419707245191433497978);
+/// assert_eq!(n.mean(), 0.0);
+/// assert_relative_eq!(n.pdf(1.0), 0.2419707245191433497978);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Normal {
diff --git a/src/distribution/pareto.rs b/src/distribution/pareto.rs
index 22a8de86..e056d8f9 100644
--- a/src/distribution/pareto.rs
+++ b/src/distribution/pareto.rs
@@ -9,12 +9,12 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{Pareto, Continuous};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let p = Pareto::new(1.0, 2.0).unwrap();
-/// assert_eq!(p.mean().unwrap(), 2.0);
-/// assert!(prec::almost_eq(p.pdf(2.0), 0.25, 1e-15));
+/// assert_eq!(p.mean(), Some(2.0));
+/// assert_relative_eq!(p.pdf(2.0), 0.25);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Pareto {
@@ -223,11 +223,7 @@ impl Max<f64> for Pareto {
 /// # Formula
 ///
 /// ```text
-/// if α <= 1 {
-///     f64::INFINITY
-/// } else {
-///     (α * x_m)/(α - 1)
-/// }
+///     (α * x_m)/(α - 1), where α > 1
 /// ```
 ///
 /// where `x_m` is the scale and `α` is the shape
diff --git a/src/distribution/poisson.rs b/src/distribution/poisson.rs
index b8ed6c77..36f2c877 100644
--- a/src/distribution/poisson.rs
+++ b/src/distribution/poisson.rs
@@ -10,12 +10,12 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{Poisson, Discrete};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = Poisson::new(1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 1.0);
-/// assert!(prec::almost_eq(n.pmf(1), 0.367879441171442, 1e-15));
+/// assert_eq!(n.mean(), 1.0);
+/// assert_relative_eq!(n.pmf(1), 0.367879441171442, epsilon=1e-14);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Poisson {
diff --git a/src/distribution/students_t.rs b/src/distribution/students_t.rs
index 99991b72..f11e6e8a 100644
--- a/src/distribution/students_t.rs
+++ b/src/distribution/students_t.rs
@@ -10,12 +10,12 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{StudentsT, Continuous};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = StudentsT::new(0.0, 1.0, 2.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 0.0);
-/// assert!(prec::almost_eq(n.pdf(0.0), 0.353553390593274, 1e-15));
+/// assert_eq!(n.mean(), Some(0.0));
+/// assert_relative_eq!(n.pdf(0.0), 0.353553390593274, epsilon=1e-14);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct StudentsT {
diff --git a/src/distribution/triangular.rs b/src/distribution/triangular.rs
index ba306807..268c9969 100644
--- a/src/distribution/triangular.rs
+++ b/src/distribution/triangular.rs
@@ -10,10 +10,10 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{Triangular, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::statistics::*;
 ///
 /// let n = Triangular::new(0.0, 5.0, 2.5).unwrap();
-/// assert_eq!(n.mean().unwrap(), 7.5 / 3.0);
+/// assert_eq!(n.mean(), 7.5 / 3.0);
 /// assert_eq!(n.pdf(2.5), 5.0 / 12.5);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
diff --git a/src/distribution/uniform.rs b/src/distribution/uniform.rs
index 10df74bb..6289948f 100644
--- a/src/distribution/uniform.rs
+++ b/src/distribution/uniform.rs
@@ -11,10 +11,10 @@ use std::fmt::Debug;
 ///
 /// ```
 /// use statrs::distribution::{Uniform, Continuous};
-/// use statrs::statistics::Distribution;
+/// use statrs::statistics::*;
 ///
 /// let n = Uniform::new(0.0, 1.0).unwrap();
-/// assert_eq!(n.mean().unwrap(), 0.5);
+/// assert_eq!(n.mean(), 0.5);
 /// assert_eq!(n.pdf(0.5), 1.0);
 /// ```
 #[derive(Debug, Copy, Clone, PartialEq)]
diff --git a/src/distribution/weibull.rs b/src/distribution/weibull.rs
index 6a70abd9..ed2f29a6 100644
--- a/src/distribution/weibull.rs
+++ b/src/distribution/weibull.rs
@@ -11,13 +11,12 @@ use std::f64;
 ///
 /// ```
 /// use statrs::distribution::{Weibull, Continuous};
-/// use statrs::statistics::Distribution;
-/// use statrs::prec;
+/// use statrs::statistics::*;
+/// use approx::assert_relative_eq;
 ///
 /// let n = Weibull::new(10.0, 1.0).unwrap();
-/// assert!(prec::almost_eq(n.mean().unwrap(),
-/// 0.95135076986687318362924871772654021925505786260884, 1e-15));
-/// assert_eq!(n.pdf(1.0), 3.6787944117144232159552377016146086744581113103177);
+/// assert_relative_eq!(n.mean(), 0.951350769866873183629, epsilon = 1e-14);
+/// assert_relative_eq!(n.pdf(1.0), 3.67879441171442321595, epsilon = 1e-14);
 /// ```
 #[derive(Copy, Clone, PartialEq, Debug)]
 pub struct Weibull {
diff --git a/src/lib.rs b/src/lib.rs
index d4d80ebc..59942837 100644
--- a/src/lib.rs
+++ b/src/lib.rs
@@ -20,13 +20,13 @@
 //! Statrs also comes with a number of useful utility traits for more detailed introspection of distributions.
 //! ```
 //! use statrs::distribution::{Exp, Continuous, ContinuousCDF}; // `cdf` and `pdf`
-//! use statrs::statistics::Distribution; // statistical moments and entropy
+//! use statrs::statistics::*; // statistical moments and entropy
 //!
 //! let n = Exp::new(1.0).unwrap();
-//! assert_eq!(n.mean(), Some(1.0));
-//! assert_eq!(n.variance(), Some(1.0));
-//! assert_eq!(n.entropy(), Some(1.0));
-//! assert_eq!(n.skewness(), Some(2.0));
+//! assert_eq!(n.mean(), 1.0);
+//! assert_eq!(n.variance(), 1.0);
+//! assert_eq!(n.entropy(), 1.0);
+//! assert_eq!(n.skewness(), 2.0);
 //! assert_eq!(n.cdf(1.0), 0.6321205588285576784045);
 //! assert_eq!(n.pdf(1.0), 0.3678794411714423215955);
 //! ```
@@ -36,7 +36,7 @@
 //!
 //! ```
 //! use statrs::distribution::FisherSnedecor;
-//! use statrs::statistics::Distribution;
+//! use statrs::statistics::*;
 //!
 //! let n = FisherSnedecor::new(1.0, 1.0).unwrap();
 //! assert!(n.variance().is_none());