Struct Cauchy 

pub struct Cauchy {
    pub location: Ex,
    pub scale: Ex,
}

Cauchy(x₀, γ): density 1 / (πγ (1 + ((x−x₀)/γ)²)) on ℝ. No moments of any order exist.

Fields

location: Ex

Location x₀ (the median).

scale: Ex

Scale γ > 0 (half the interquartile range).

Trait Implementations

impl Clone for Cauchy

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Cauchy

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

Formats the value using the given formatter.

impl Family for Cauchy

fn name(&self) -> &str

The family’s name ("Normal", "Binomial", …).

fn context(&self) -> Context

The context the parameters live in (a cheap handle clone).

fn parameters(&self) -> Vec<(&'static str, Ex)>

The parameters, named, in the family’s documented order.

fn eq_family(&self, other: &dyn Family) -> bool

Structural equality with another family (see same_family).

fn support(&self) -> Support

Where the mass is.

fn density(&self, x: &Ex) -> Ex

The density (continuous) or probability mass function (discrete) as an expression in x, valid on the support.

fn cdf(&self, x: &Ex) -> Option<Ex>

Closed-form P(X ≤ x) for x in the support.

fn quantile(&self, p: &Ex) -> Option<Ex>

Closed-form quantile function (inverse CDF) at p ∈ (0, 1).

fn entropy(&self) -> Option<Ex>

Closed-form entropy (differential for a continuous family, Shannon for a discrete one), in nats.

fn mean(&self) -> Option<Ex>

Closed-form mean.

fn variance(&self) -> Option<Ex>

Closed-form variance.

fn raw_moment(&self, _n: u32) -> Option<Ex>

Closed-form raw moment E[Xⁿ], n ≥ 1.

fn mgf(&self, _t: &Ex) -> Option<Ex>

Closed-form moment generating function E[e^{tX}].

fn probability_of(&self, _region: &Support) -> Option<Result<Ex, SymplexError>>

P(X ∈ region) when the family can answer more directly than by integrating its density over support ∩ region (a mixture sums its components). None leaves it to the generic route.

fn expectation_over( &self, _g: &Ex, _x: &Ex, _region: &Support, ) -> Option<Result<Ex, SymplexError>>

E[g(X)·1_{X ∈ region}] for g in the symbol x, when the family can answer directly. None leaves it to the generic route.

fn sampler(&self) -> Option<Result<Sampler, SymplexError>>

A sampler, when the family has a route of its own (a wrapper transforms its inner family’s samples). None leaves it to the generic route: inverse transform through the quantile, or cumulative sums of the mass function.

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

Name(p₁, p₂, …).

impl PartialEq for Cauchy

fn eq(&self, other: &Self) -> bool

Equality operator ==.

fn ne(&self, other: &Rhs) -> bool

Inequality operator !=.

impl StructuralPartialEq for Cauchy