mathru 0.16.2

Fundamental algorithms for scientific computing in Rust
Documentation 
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//! Exponential distribution
use crate::{algebra::abstr::Real, statistics::distrib::Continuous};
use rand;
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
use std::clone::Clone;

/// Exponential distribution
///
/// Fore more information:
/// <https://en.wikipedia.org/wiki/Exponential_distribution>
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Copy, Debug)]
pub struct Exponential<T> {
    lambda: T,
}

impl<T> Exponential<T>
where
    T: Real,
{
    /// Creates a probability distribution
    ///
    /// # Arguments
    ///
    /// * `lambda`  > 0.0
    ///
    /// # Panics
    ///
    /// if lambda <= 0.0
    ///
    /// # Example
    ///
    /// ```
    /// use mathru::statistics::distrib::Exponential;
    ///
    /// let distrib: Exponential<f64> = Exponential::new(0.3);
    /// ```
    pub fn new(lambda: T) -> Exponential<T> {
        if lambda <= T::zero() {
            panic!()
        }

        Exponential { lambda }
    }

    pub fn from_data(data: &[T]) -> Self {
        let lambda: T = T::one() / Exponential::calc_mean(data);

        Exponential::new(lambda)
    }

    fn calc_mean(data: &[T]) -> T {
        let mut sum: T = T::zero();

        for x in data.iter() {
            sum += *x;
        }

        sum / T::from_u64(data.len() as u64)
    }
}

impl<T> Continuous<T> for Exponential<T>
where
    T: Real,
{
    /// Probability density function
    ///
    /// # Arguments
    ///
    /// * `x` Random variable x &isin; &#x2115 | x > 0.0
    ///
    /// # Example
    ///
    /// ```
    /// use mathru::statistics::distrib::{Continuous, Exponential};
    ///
    /// let distrib: Exponential<f64> = Exponential::new(0.3);
    /// let x: f64 = 5.0;
    /// let p: f64 = distrib.pdf(x);
    /// ```
    fn pdf(&self, x: T) -> T {
        if x < T::zero() {
            return T::zero();
        }

        self.lambda * (-self.lambda * x).exp()
    }

    /// Cumulative distribution function
    ///
    /// # Arguments
    ///
    /// * `x` Random variable
    ///
    /// # Example
    ///
    /// ```
    /// use mathru::statistics::distrib::{Continuous, Exponential};
    ///
    /// let distrib: Exponential<f64> = Exponential::new(0.3);
    /// let x: f64 = 0.4;
    /// let p: f64 = distrib.cdf(x);
    /// ```
    fn cdf(&self, x: T) -> T {
        if x < T::zero() {
            return T::zero();
        }

        T::one() - (-x * self.lambda).exp()
    }

    /// Quantile function of inverse cdf
    fn quantile(&self, p: T) -> T {
        -(T::one() - p).ln() / self.lambda
    }

    /// Expected value
    ///
    /// # Example
    ///
    /// ```
    /// use mathru::statistics::distrib::{Continuous, Exponential};
    ///
    /// let distrib: Exponential<f64> = Exponential::new(0.2);
    /// let mean: f64 = distrib.mean();
    /// ```
    fn mean(&self) -> T {
        T::one() / self.lambda
    }

    /// Variance
    ///
    /// # Example
    ///
    /// ```
    /// use mathru::statistics::distrib::{Continuous, Exponential};
    ///
    /// let distrib: Exponential<f64> = Exponential::new(0.2);
    /// let var: f64 = distrib.variance();
    /// ```
    fn variance(&self) -> T {
        T::one() / self.lambda.pow(T::from_u8(2))
    }

    fn skewness(&self) -> T {
        T::from_f64(2.0)
    }

    fn median(&self) -> T {
        T::from_f64(2.0).ln() / self.lambda
    }

    fn entropy(&self) -> T {
        T::one() - self.lambda.ln()
    }
}

impl<T> Exponential<T>
where
    T: Real,
{
    pub fn random(&self) -> T {
        let y: T = T::from_f64(rand::random::<f64>());
        let p: T = self.quantile(y);

        p
    }
}