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//! Bernoulli Distribution
use crate::{algebra::abstr::Real, statistics::distrib::Discrete};
#[cfg(feature = "serde")]
use serde::{Deserialize, Serialize};
use std::clone::Clone;
/// Bernoulli distribution
///
/// Fore more information:
///
/// <https://en.wikipedia.org/wiki/Bernoulli_distribution>
#[cfg_attr(feature = "serde", derive(Serialize, Deserialize))]
#[derive(Clone, Copy, Debug)]
pub struct Bernoulli<T> {
p: T,
}
impl<T> Bernoulli<T>
where
T: Real,
{
/// Create a probability distribution with p(X=1) = p
///
/// # Arguments
///
/// * `p` Probability that random varibale X=1, 0.0 <= p <= 1.0
///
/// # Panics
///
/// if p < 0 || p > 1.0
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::Bernoulli;
///
/// let distrib: Bernoulli<f64> = Bernoulli::new(0.2);
/// ```
pub fn new(p: T) -> Bernoulli<T> {
if p < T::zero() || p > T::one() {
panic!()
}
Bernoulli { p }
}
}
impl<T> Discrete<T, u8, T> for Bernoulli<T>
where
T: Real,
{
/// Probability mass function of the Bernoulli distribution
///
///
/// # Arguments
///
/// * `x` Random variable x ∈ {0, 1}
///
/// # Panics
///
/// if x ∉ {0, 1}
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Bernoulli, Discrete};
///
/// let distrib: Bernoulli<f64> = Bernoulli::new(0.2);
/// let x: u8 = 0;
/// let p: f64 = distrib.pmf(x);
/// ```
fn pmf(&self, x: u8) -> T {
if (x == 1) || (x == 0) {
if x == 0 {
T::one() - self.p
} else {
self.p
}
} else {
panic!()
}
}
/// Cumulative distribution function of the Bernoulli distribution
///
/// # Arguments
///
/// * `x` Random variable x ∈ {0, 1}
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Bernoulli, Discrete};
///
/// let distrib: Bernoulli<f64> = Bernoulli::new(0.2);
/// let x: f64 = 0.4;
/// let p: f64 = distrib.cdf(x);
/// ```
fn cdf(&self, x: T) -> T {
if x >= T::one() {
return T::one();
}
if x <= T::zero() {
T::zero()
} else {
T::one() - self.p
}
}
/// Expected value
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Bernoulli, Discrete};
///
/// let distrib: Bernoulli<f64> = Bernoulli::new(0.2);
/// let mean: f64 = distrib.mean();
/// ```
fn mean(&self) -> T {
self.p
}
/// Variance
///
/// # Example
///
/// ```
/// use mathru::statistics::distrib::{Bernoulli, Discrete};
///
/// let distrib: Bernoulli<f64> = Bernoulli::new(0.2);
/// let var: f64 = distrib.variance();
/// ```
fn variance(&self) -> T {
self.p * (T::one() - self.p)
}
}