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use crate::{ consts::THREE_HALVES, prelude::*, }; use rand::Rng; use spaces::real::PositiveReals; use std::fmt; pub use crate::params::DOF; new_dist!(Chi<DOF<usize>>); macro_rules! get_k { ($self:ident) => { ($self.0).0 as f64 } } impl Chi { pub fn new(dof: usize) -> Result<Chi, failure::Error> { Ok(Chi(DOF::new(dof)?)) } pub fn new_unchecked(dof: usize) -> Chi { Chi(DOF(dof)) } #[inline(always)] pub fn k(&self) -> f64 { get_k!(self) } } impl Distribution for Chi { type Support = PositiveReals; type Params = DOF<usize>; fn support(&self) -> PositiveReals { PositiveReals } fn params(&self) -> DOF<usize> { self.0 } fn cdf(&self, x: &f64) -> Probability { use special_fun::FloatSpecial; Probability::new_unchecked((get_k!(self) / 2.0).gammainc(x * x / 2.0)) } fn sample<R: Rng + ?Sized>(&self, _: &mut R) -> f64 { unimplemented!() } } impl ContinuousDistribution for Chi { fn pdf(&self, x: &f64) -> f64 { use special_fun::FloatSpecial; let k = get_k!(self); let ko2 = k / 2.0; let norm = 2.0f64.powf(ko2 - 1.0) * ko2.gamma(); x.powf(k - 1.0) * (-x * x / 2.0).exp() / norm } } impl UnivariateMoments for Chi { fn mean(&self) -> f64 { use special_fun::FloatSpecial; let k = get_k!(self); 2.0f64.sqrt() * ((k + 1.0) / 2.0).gamma() / (k / 2.0).gamma() } fn variance(&self) -> f64 { let k = get_k!(self); let mu = self.mean(); k - mu * mu } fn skewness(&self) -> f64 { let mu = self.mean(); let var = self.variance(); mu / var.powf(THREE_HALVES) * (1.0 - 2.0 * var) } fn excess_kurtosis(&self) -> f64 { let mu = self.mean(); let var = self.variance(); let std = var.sqrt(); let skewness = self.skewness(); 2.0 / var * (1.0 - mu * std * skewness - var) } } impl Quantiles for Chi { fn quantile(&self, _: Probability) -> f64 { unimplemented!() } fn median(&self) -> f64 { let k = get_k!(self); (k * (1.0 - 2.0 / 9.0 / k).powi(3)).sqrt() } } impl Modes for Chi { fn modes(&self) -> Vec<f64> { let k = (self.0).0; if k >= 1 { vec![((k - 1) as f64).sqrt()] } else { vec![] } } } impl Entropy for Chi { fn entropy(&self) -> f64 { use special_fun::FloatSpecial; let k = get_k!(self); let ko2 = k / 2.0; ko2.gamma().ln() + (k - 2.0f64.ln() - (k - 1.0) * ko2.digamma()) } } impl fmt::Display for Chi { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { write!(f, "Chi({})", self.k()) } }