refactor!: decouple distribution traits from rand

This changes the behavior of Cauchy::mean() and Cauchy::variance()
from the old default implementation (based on RNG sampling) to simply
returning `None`. Both mean and variance are undefined for the cauchy
distribution.

This also changes the trait signature of both Distribution<T> and
DiscreteDistribution<T> to not be subtraits of
rand::distribution::Distribution<T>. Our distributions do still
implement this trait iff the `rand` feature is enabled.

Author: FreezyLemon

src/statistics/traits.rs

@@ -1,7 +1,5 @@
 use ::num_traits::float::Float;
 
-const STEPS: usize = 1_000;
-
 /// The `Min` trait specifies than an object has a minimum value
 pub trait Min<T> {
     /// Returns the minimum value in the domain of a given distribution
@@ -35,7 +33,7 @@ pub trait Max<T> {
     /// ```
     fn max(&self) -> T;
 }
-pub trait DiscreteDistribution<T: Float>: ::rand::distributions::Distribution<u64> {
+pub trait DiscreteDistribution<T: Float> {
     /// Returns the mean, if it exists.
     fn mean(&self) -> Option<T> {
         None
@@ -58,14 +56,8 @@ pub trait DiscreteDistribution<T: Float>: ::rand::distributions::Distribution<u6
     }
 }
 
-pub trait Distribution<T: Float>: ::rand::distributions::Distribution<T> {
+pub trait Distribution<T: Float> {
     /// Returns the mean, if it exists.
-    /// The default implementation returns an estimation
-    /// based on random samples. This is a crude estimate
-    /// for when no further information is known about the
-    /// distribution. More accurate statements about the
-    /// mean can and should be given by overriding the
-    /// default implementation.
     ///
     /// # Examples
     ///
@@ -77,23 +69,9 @@ pub trait Distribution<T: Float>: ::rand::distributions::Distribution<T> {
     /// assert_eq!(0.5, n.mean().unwrap());
     /// ```
     fn mean(&self) -> Option<T> {
-        // TODO: Does not need cryptographic rng
-        let mut rng = ::rand::rngs::OsRng;
-        let mut mean = T::zero();
-        let mut steps = T::zero();
-        for _ in 0..STEPS {
-            steps = steps + T::one();
-            mean = mean + Self::sample(self, &mut rng);
-        }
-        Some(mean / steps)
+        None
     }
     /// Returns the variance, if it exists.
-    /// The default implementation returns an estimation
-    /// based on random samples. This is a crude estimate
-    /// for when no further information is known about the
-    /// distribution. More accurate statements about the
-    /// variance can and should be given by overriding the
-    /// default implementation.
     ///
     /// # Examples
     ///
@@ -105,19 +83,7 @@ pub trait Distribution<T: Float>: ::rand::distributions::Distribution<T> {
     /// assert_eq!(1.0 / 12.0, n.variance().unwrap());
     /// ```
     fn variance(&self) -> Option<T> {
-        // TODO: Does not need cryptographic rng
-        let mut rng = ::rand::rngs::OsRng;
-        let mut mean = T::zero();
-        let mut variance = T::zero();
-        let mut steps = T::zero();
-        for _ in 0..STEPS {
-            steps = steps + T::one();
-            let sample = Self::sample(self, &mut rng);
-            variance = variance + (steps - T::one()) * (sample - mean) * (sample - mean) / steps;
-            mean = mean + (sample - mean) / steps;
-        }
-        steps = steps - T::one();
-        Some(variance / steps)
+        None
     }
     /// Returns the standard deviation, if it exists.
     ///