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//! Probability distributions and statistics in Rust with integrated fitting //! routines, convolution support and mixtures. // #![warn(missing_docs)] extern crate failure; extern crate rand; extern crate rand_distr; extern crate num; extern crate special_fun; extern crate spaces; extern crate ndarray; #[cfg(feature = "ndarray-linalg")] extern crate ndarray_linalg; #[cfg_attr(feature = "serde", macro_use)] #[cfg(feature = "serde")] extern crate serde_crate; macro_rules! undefined { () => (panic!("quantity undefined")); ($($arg:tt)+) => (panic!("quantity undefined: {}", std::format_args!($($arg)+))); } mod consts; mod utils; pub mod linalg; mod probability; pub use self::probability::{ InvalidProbabilityError, Probability, InvalidSimplexError, SimplexVector, UnitSimplex, }; #[macro_use] pub mod params; /// Iterator for drawing random samples from a /// [distribution](trait.Distribution.html). pub struct Sampler<'a, D: ?Sized, R: ?Sized> { pub(crate) distribution: &'a D, pub(crate) rng: &'a mut R, } impl<'a, D, R> Iterator for Sampler<'a, D, R> where D: Distribution + ?Sized, R: rand::Rng + ?Sized, { type Item = <D::Support as spaces::Space>::Value; #[inline(always)] fn next(&mut self) -> Option<Self::Item> { Some(self.distribution.sample(&mut self.rng)) } fn size_hint(&self) -> (usize, Option<usize>) { (usize::max_value(), None) } } macro_rules! ln_variant { ($(#[$attr:meta])* => $name:ident, $name_ln:ident, $x:ty) => { $(#[$attr])* fn $name_ln(&self, x: $x) -> f64 { self.$name(x).ln() } } } /// Type alias for the sample type of a [distribution](trait.Distribution.html). pub type Sample<D> = <<D as Distribution>::Support as spaces::Space>::Value; /// Trait for probability distributions with a well-defined CDF. pub trait Distribution: From<<Self as Distribution>::Params> { /// Support of sample elements. type Support: spaces::Space; /// Parameter set uniquely defining the instance. type Params; /// Returns an instance of the support `Space`, `Self::Support`. /// /// # Examples /// ``` /// # use spaces::{Space, BoundedSpace, Dim}; /// # use rstat::{Distribution, univariate, params::Param}; /// let dist = univariate::beta::Beta::default(); /// let support = dist.support(); /// /// assert_eq!(support.dim(), Dim::Finite(1)); /// assert_eq!(support.inf().unwrap(), 0.0); /// assert_eq!(support.sup().unwrap(), 1.0); /// ``` fn support(&self) -> Self::Support; /// Converts `self` into an instance of `Self::Support`. fn into_support(self) -> Self::Support { self.support() } /// Returns an instance of the distribution parameters, `Self::Params`. /// /// # Examples /// ``` /// # use rstat::{Distribution, univariate, params::Param}; /// let dist = univariate::normal::Normal::standard(); /// let params = dist.params(); /// /// assert_eq!(params.mu.value(), &0.0); /// assert_eq!(params.Sigma.value(), &1.0); /// ``` fn params(&self) -> Self::Params; /// Converts `self` into an instance of `Self::Params`. fn into_params(self) -> Self::Params { self.params() } /// Evaluates the cumulative distribution function (CDF) at \\(x\\). /// /// The CDF is defined as the probability that a random variable \\(X\\) /// takes on a value less than or equal to \\(x\\), i.e. \\(F(x) = P(X /// \leq x)\\). /// /// # Examples /// ``` /// # use rstat::{Distribution, Probability, univariate}; /// # use std::f64; /// let dist = univariate::normal::Normal::standard(); /// /// assert_eq!(dist.cdf(&f64::NEG_INFINITY), Probability::zero()); /// assert_eq!(dist.cdf(&0.0), Probability::half()); /// assert_eq!(dist.cdf(&f64::INFINITY), Probability::one()); /// ``` fn cdf(&self, x: &Sample<Self>) -> Probability { Probability::new_unchecked(self.log_cdf(x).exp()) } /// Evaluates the complementary CDF at \\(x\\). /// /// The complementary CDF (also known as the survival function) is defined /// as the probability that a random variable \\(X\\) takes on a value /// strictly greater than \\(x\\), i.e. \\(\bar{F}(x) = P(X > x) = 1 - /// F(x)\\). fn ccdf(&self, x: &Sample<Self>) -> Probability { !self.cdf(x) } ln_variant!( /// Evaluates the log CDF at \\(x\\), i.e. \\(\ln{F(x)}\\). => cdf, log_cdf, &Sample<Self> ); ln_variant!( /// Evaluates the log complementary CDF at \\(x\\), i.e. \\(\ln{(1 - F(x))}\\). => ccdf, log_ccdf, &Sample<Self> ); /// Draw a random value from the distribution support. fn sample<R: rand::Rng + ?Sized>(&self, rng: &mut R) -> Sample<Self>; /// Draw n random value from the distribution support. fn sample_n<R: rand::Rng + ?Sized>(&self, rng: &mut R, n: usize) -> Vec<Sample<Self>> { (0..n).into_iter().map(move |_| self.sample(rng)).collect() } /// Draw an indefinite number of random values from the distribution /// support. fn sample_iter<'a, R: rand::Rng + ?Sized>(&'a self, rng: &'a mut R) -> Sampler<'a, Self, R> { Sampler { distribution: self, rng, } } } macro_rules! new_dist { ($(#[$attr:meta])* $name:ident<$pt:ty>) => { $(#[$attr])* #[derive(Debug, Clone)] pub struct $name(pub(crate) $pt); impl From<$pt> for $name { fn from(from: $pt) -> $name { $name(from) } } }; } #[inline] pub fn params_of<D: Distribution>(dist: &D) -> D::Params { dist.params() } #[inline] pub fn support_of<D: Distribution>(dist: &D) -> D::Support { dist.support() } /// Trait for [distributions](trait.Distribution.html) over a countable /// `Support`. /// /// The PMF is defined as the probability that a random variable \\(X\\) takes a /// value exactly equal to \\(x\\), i.e. \\(f(x) = P(X = x) = P(s \in S : X(s) = /// x)\\). We require that all sum of probabilities over all possible outcomes /// sums to 1. pub trait DiscreteDistribution: Distribution { /// Evaluates the probability mass function (PMF) at \\(x\\). /// /// # Examples /// ``` /// # use rstat::{DiscreteDistribution, Probability, univariate::binomial::Binomial}; /// let dist = Binomial::new_unchecked(5, Probability::new_unchecked(0.75)); /// /// assert_eq!(dist.pmf(&0), Probability::new_unchecked(0.0009765625)); /// assert_eq!(dist.pmf(&1), Probability::new_unchecked(0.0146484375)); /// assert_eq!(dist.pmf(&2), Probability::new_unchecked(0.087890625)); /// assert_eq!(dist.pmf(&3), Probability::new_unchecked(0.263671875)); /// assert_eq!(dist.pmf(&4), Probability::new_unchecked(0.3955078125)); /// assert_eq!(dist.pmf(&5), Probability::new_unchecked(0.2373046875)); /// ``` fn pmf(&self, x: &Sample<Self>) -> Probability { Probability::new_unchecked(self.log_pmf(x).exp()) } ln_variant!( /// Evaluates the log PMF at \\(x\\). => pmf, log_pmf, &Sample<Self> ); } /// Trait for [distributions](trait.Distribution.html) with an absolutely /// continuous CDF. /// /// The PDF can be interpreted as the relative likelihood that a random variable /// \\(X\\) takes on a value equal to \\(x\\). For absolutely continuous /// univariate distributions it is defined by the derivative of the CDF, i.e /// \\(f(x) = F'(x)\\). Intuitively, one may think of \\(f(x)\text{d}x\\) that /// as representing the probability that the random variable \\(X\\) lies in the /// infinitesimal interval \\([x, x + \text{d}x]\\). Alternatively, one can /// interpret the PDF, for infinitesimally small \\(\text{d}t\\), as: /// \\(f(t)\text{d}t = P(t < X < t + \text{d}t)\\). For a finite interval \\([a, /// b],\\) we have that: \\[P(a < X < b) = \int_a^b f(t)\text{d}t.\\] pub trait ContinuousDistribution: Distribution { /// Evaluates the probability density function (PDF) at \\(x\\). /// /// # Examples /// ``` /// # use rstat::{ContinuousDistribution, Probability, univariate::triangular::Triangular}; /// let dist = Triangular::new_unchecked(0.0, 0.5, 0.5); /// /// assert_eq!(dist.pdf(&0.0), 0.0); /// assert_eq!(dist.pdf(&0.25), 1.0); /// assert_eq!(dist.pdf(&0.5), 2.0); /// assert_eq!(dist.pdf(&0.75), 1.0); /// assert_eq!(dist.pdf(&1.0), 0.0); /// ``` fn pdf(&self, x: &Sample<Self>) -> f64 { self.log_pdf(x).exp() } ln_variant!( /// Evaluates the log PDF at \\(x\\). => pdf, log_pdf, &Sample<Self> ); } /// Trait for [distributions](trait.Distribution.html) that support the convolve /// operation. /// /// The convolution of probability [distributions](trait.Distribution.html) /// amounts to taking linear combinations of independent random variables. For /// example, consider a set of \\(N\\) random variables \\(X_i \sim /// \text{Bernoulli}(p)\\), where \\(p \in (0, 1)\\) and \\(1 \leq i \leq N\\). /// We then have that the random variables \\(Y = \sum_{i=1}^N X_i\\) and \\(Z /// \sim \text{Binomial}(N, p)\\) are exactly equivalent, i.e. \\(Y /// \stackrel{\text{d}}{=} Z\\). pub trait Convolution<T: Distribution = Self> { /// The resulting [Distribution](trait.Distribution.html) type. type Output: Distribution; /// Return the unweighted linear sum of `self` with another /// [Distribution](trait.Distribution.html) of type `T`. /// /// # Examples /// ``` /// # use rstat::{Distribution, Convolution, params::Param, univariate::normal::Normal}; /// let dist_a = Normal::new_unchecked(0.0, 1.0f64.powi(2)); /// let dist_b = Normal::new_unchecked(1.0, 2.0f64.powi(2)); /// /// let dist_c = dist_a.convolve(dist_b).unwrap(); /// let params = dist_c.params(); /// /// assert_eq!(params.mu.value(), &1.0); /// assert_eq!(params.Sigma.value(), &5.0f64); /// ``` fn convolve(self, rv: T) -> Result<Self::Output, failure::Error>; /// Return the unweighted linear sum of `self` with a set of /// [Distributions](trait.Distribution.html) of type `T`. fn convolve_many(self, mut rvs: Vec<T>) -> Result<Self::Output, failure::Error> where Self::Output: Convolution<T, Output = Self::Output>, Self: Sized, { let n = rvs.len(); let _ = assert_constraint!(n > 1).map_err(|e| e.with_target("n"))?; let new_dist = self.convolve(rvs.pop().unwrap()); rvs.into_iter() .fold(new_dist, |acc, rv| acc.and_then(|d| d.convolve(rv))) } } pub mod metrics; pub mod statistics; pub mod fitting; pub mod normal; pub mod univariate; pub mod bivariate; pub mod multivariate; mod mixture; pub use self::mixture::Mixture; pub mod builder;