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use crate::{algebra::abstr::Real, statistics::distrib::Continuous};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
use std::clone::Clone;
/// Raised Cosine distribution
///
/// Fore more information:
/// <https://en.wikipedia.org/wiki/Raised_cosine_distribution>
///
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Copy, Debug)]
pub struct RaisedCosine<T> {
mu: T,
s: T,
}
impl<T> RaisedCosine<T>
where
T: Real,
{
/// Creates a probability distribution
///
/// # Arguments
///
/// * `mu`
/// * `s` > 0.0
///
/// # Panics
///
/// if s < 0.0
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::RaisedCosine;
/// use std::f64::consts::PI;
///
/// let mu: f64 = PI;
/// let s: f64 = 0.5 * PI;
/// let distrib: RaisedCosine<f64> = RaisedCosine::new(mu, s);
/// ```
pub fn new(mu: T, s: T) -> RaisedCosine<T> {
if s < T::zero() {
panic!();
}
RaisedCosine { mu, s }
}
}
impl<T> Continuous<T> for RaisedCosine<T>
where
T: Real,
{
/// Probability density function
///
/// # Arguments
///
/// * `x` Random variable x
///
/// # Panics
///
///
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, RaisedCosine};
///
/// let distrib: RaisedCosine<f64> = RaisedCosine::new(-1.2, 1.5);
/// let x: f64 = 5.0;
/// let p: f64 = distrib.pdf(x);
/// ```
fn pdf(&self, x: T) -> T {
if (self.mu - self.s) <= x && x < (self.mu + self.s) {
return (T::one() + (T::pi() * (x - self.mu) / self.s).cos())
/ (T::from_f64(2.0) * self.s);
}
T::zero()
}
/// Cumulative distribution function
///
/// # Arguments
///
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, RaisedCosine};
/// use std::f64::consts::PI;
///
/// let distrib: RaisedCosine<f64> = RaisedCosine::new(1.0, PI);
/// let x: f64 = PI / 2.0;
/// let p: f64 = distrib.cdf(x);
/// ```
fn cdf(&self, x: T) -> T {
if (self.mu - self.s) <= x && x <= (self.mu + self.s) {
let k: T = (x - self.mu) / self.s;
(T::one() + k + T::one() / T::pi() * (k * T::pi()).sin()) / T::from_f64(2.0)
} else if x < (self.mu - self.s) {
T::zero()
} else {
T::one()
}
}
/// Quantile function of inverse cdf
fn quantile(&self, _p: T) -> T {
unimplemented!();
}
/// Expected value
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, RaisedCosine};
///
/// let distrib: RaisedCosine<f64> = RaisedCosine::new(-2.0, 0.5);
/// let mean: f64 = distrib.mean();
/// ```
fn mean(&self) -> T {
self.mu
}
/// Variance
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Continuous, RaisedCosine};
/// use std::f64::consts::PI;
///
/// let distrib: RaisedCosine<f64> = RaisedCosine::new(2.0, PI);
/// let var: f64 = distrib.variance();
/// ```
fn variance(&self) -> T {
self.s * self.s * (T::from_f64(1.0 / 3.0) - T::from_f64(2.0) / (T::pi() * T::pi()))
}
fn skewness(&self) -> T {
T::zero()
}
/// Median is the value separating the higher half from the lower half of a
/// probability distribution.
fn median(&self) -> T {
self.mu
}
fn entropy(&self) -> T {
unimplemented!();
}
}