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// Beta distribution
use crate::{algebra::abstr::Real, special, special::beta, statistics::distrib::Continuous};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
use std::clone::Clone;
/// Beta distribution
///
/// Fore more information:
/// <https://en.wikipedia.org/wiki/Beta_distribution>
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Copy, Debug)]
pub struct Beta<T> {
p: T,
q: T,
}
impl<T> Beta<T>
where
T: Real,
{
/// Create a probability distribution
///
/// # Arguments
///
/// * `p`: α > 0.0
/// * `q`: β > 0.0
///
/// # Panics
/// if p <= 0.0 || q <= 0.0
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Beta, Continuous};
///
/// let distrib: Beta<f64> = Beta::new(0.2, 0.3);
/// ```
pub fn new(p: T, q: T) -> Beta<T> {
if p < T::zero() || q <= T::zero() {
panic!()
}
Beta { p, q }
}
}
impl<T> Continuous<T> for Beta<T>
where
T: Real + beta::Beta,
{
/// Probability density function
///
/// # Arguments
///
/// * `x` &isin ࡃ
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Beta, Continuous};
///
/// let distrib: Beta<f64> = Beta::new(0.2, 0.3);
/// let x: f64 = 0.5;
/// let p: f64 = distrib.pdf(x);
/// ```
fn pdf(&self, x: T) -> T {
if x < T::zero() {
panic!();
}
if x > T::one() {
return T::one();
}
x.pow(self.p - T::one()) * (T::one() - x).pow(self.q - T::one())
/ special::beta::beta(self.p, self.q)
}
/// Cumulative distribution function
///
/// # Arguments
///
/// * `x`
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Beta, Continuous};
///
/// let distrib: Beta<f64> = Beta::new(0.3, 0.2);
/// let x: f64 = 0.4;
/// let p: f64 = distrib.cdf(x);
/// ```
fn cdf(&self, x: T) -> T {
beta::beta_inc_reg(x, self.p, self.q)
}
/// Quantile function of inverse cdf
fn quantile(&self, _p: T) -> T {
unimplemented!();
}
/// Expected value
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Beta, Continuous};
///
/// let distrib: Beta<f64> = Beta::new(0.2, 0.3);
/// let mean: f64 = distrib.mean();
/// ```
fn mean(&self) -> T {
self.p / (self.p + self.q)
}
/// Variance
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Beta, Continuous};
///
/// let distrib: Beta<f64> = Beta::new(0.2, 0.3);
/// let var: f64 = distrib.variance();
/// ```
fn variance(&self) -> T {
self.p * self.q / ((self.p + self.q + T::one()) * (self.p + self.q).pow(T::from_f64(2.0)))
}
/// Skewness
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Beta, Continuous};
///
/// let distrib: Beta<f64> = Beta::new(0.2, 0.3);
/// let skewness: f64 = distrib.skewness();
/// ```
fn skewness(&self) -> T {
T::from_f64(2.0) * (self.q - self.p) * (self.p + self.q + T::one()).sqrt()
/ ((self.p + self.q + T::from_f64(2.0)) * (self.q * self.p).sqrt())
}
fn median(&self) -> T {
unimplemented!();
}
fn entropy(&self) -> T {
unimplemented!();
}
}