Struct StudentT 

pub struct StudentT { /* private fields */ }

Student’s t-distribution with a location and scale, StudentT(ν, μ, σ).

Heavy-tailed generalization of the Normal; as ν → ∞ it converges to Normal(μ, σ). Widely used as a robust likelihood/prior because its tails tolerate outliers. ν need not be an integer.

Mathematical Properties:

• Support: (-∞, +∞)
• PDF: f(x) = Γ((ν+1)/2) / (Γ(ν/2)·√(νπ)·σ) · (1 + z²/ν)^(-(ν+1)/2), where z = (x−μ)/σ
• Mean: μ for ν > 1 (undefined otherwise)
• Variance: σ²·ν/(ν−2) for ν > 2 (infinite for 1 < ν ≤ 2)

Example:

// Robust prior with 3 degrees of freedom.
let robust = sample(addr!("theta"), StudentT::new(3.0, 0.0, 1.0).unwrap());
// Robust likelihood tolerant of outliers.
let obs = observe(addr!("y"), StudentT::new(4.0, 1.0, 0.5).unwrap(), 2.0);

Implementations

impl StudentT

pub fn new(df: f64, loc: f64, scale: f64) -> FugueResult<Self>

Create a new Student’s t-distribution with validated parameters.

pub fn df(&self) -> f64

Get the degrees of freedom ν.

pub fn loc(&self) -> f64

Get the location parameter μ.

pub fn scale(&self) -> f64

Get the scale parameter σ.

Trait Implementations

impl Clone for StudentT

fn clone(&self) -> StudentT

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Copy for StudentT

impl Debug for StudentT

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Distribution<f64> for StudentT

fn sample(&self, rng: &mut dyn RngCore) -> f64

Generate a random sample (with its natural type), T, from the distribution, using the provided random number generator, rng.

fn log_prob(&self, x: &f64) -> LogF64

Compute the log-probability density (continuous) or mass (discrete) of a value, x, from the distribution.

fn clone_box(&self) -> Box<dyn Distribution<f64>>

Clone the distribution into a boxed trait object, Box<dyn Distribution<T>>.

impl Validate for StudentT

fn validate(&self) -> FugueResult<()>