Struct rv::dist::Gaussian

pub struct Gaussian {
    pub mu: f64,
    pub sigma: f64,
}

Gaussian / Normal distribution, N(μ, σ)

Examples

Compute the KL Divergence between two Gaussians.

use rv::prelude::*;

let gauss_1 = Gaussian::new(0.1, 2.3).unwrap();
let gauss_2 = Gaussian::standard();

// KL is not symmetric
let kl_12 = gauss_1.kl(&gauss_2);
let kl_21 = gauss_2.kl(&gauss_1);

// ... but kl_sym is because it's the sum of KL(P|Q) and KL(Q|P)
let kl_sym = gauss_1.kl_sym(&gauss_2);
assert!((kl_sym - (kl_12 + kl_21)).abs() < 1E-12);

Fields

mu: f64

Mean

sigma: f64

Standard deviation

Methods

impl Gaussian

pub fn new(mu: f64, sigma: f64) -> Result<Self>

pub fn standard() -> Self

Standard normal

Trait Implementations

impl Debug for Gaussian

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

Formats the value using the given formatter.

impl Clone for Gaussian

fn clone(&self) -> Gaussian

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Default for Gaussian

fn default() -> Self

Returns the "default value" for a type.

impl Variance<f64> for Gaussian

fn variance(&self) -> Option<f64>

Returns None if the variance is undefined

impl Entropy for Gaussian

fn entropy(&self) -> f64

The entropy, H(X)

impl Skewness for Gaussian

fn skewness(&self) -> Option<f64>

impl Kurtosis for Gaussian

fn kurtosis(&self) -> Option<f64>

impl KlDivergence for Gaussian

fn kl(&self, other: &Self) -> f64

The KL divergence, KL(P|Q) between this distribution, P, and another, Q

fn kl_sym(&self, other: &Self) -> f64

Symmetrised divergence, KL(P|Q) + KL(Q|P)

impl Rv<f32> for Gaussian

fn ln_f(&self, x: &f32) -> f64

Un-normalized probability function

fn ln_normalizer(&self) -> f64

The log of the constant term in the PDF/PMF. Should not be a function of any of the parameters.

fn draw<R: Rng>(&self, rng: &mut R) -> f32

Single draw from the Rv

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<f32>

Multiple draws of the Rv

fn f(&self, x: &X) -> f64

Un-normalized probability function

fn normalizer(&self) -> f64

The constant term in the PDF/PMF. Should not be a function of any of the parameters.

impl ContinuousDistr<f32> for Gaussian

fn pdf(&self, x: &X) -> f64

The value of the Probability Density Function (PDF) at x

fn ln_pdf(&self, x: &X) -> f64

The value of the log Probability Density Function (PDF) at x

impl Support<f32> for Gaussian

fn contains(&self, x: &f32) -> bool

Returns true if x is in the support of the Rv

impl Cdf<f32> for Gaussian

fn cdf(&self, x: &f32) -> f64

The value of the Cumulative Density Function at x

fn sf(&self, x: &X) -> f64

Survival function, 1 - CDF(x)

impl InverseCdf<f32> for Gaussian

fn invcdf(&self, p: f64) -> f32

The value of the x at the given probability in the CDF

fn quantile(&self, p: f64) -> X

Alias for invcdf

fn interval(&self, p: f64) -> (X, X)

Interval containing p proportion for the probability

impl Mean<f32> for Gaussian

fn mean(&self) -> Option<f32>

Returns None if the mean is undefined

impl Median<f32> for Gaussian

fn median(&self) -> Option<f32>

Returns None if the median is undefined

impl Mode<f32> for Gaussian

fn mode(&self) -> Option<f32>

Returns None if the mode is undefined or is not a single value

impl HasSuffStat<f32> for Gaussian

type Stat = GaussianSuffStat

fn empty_suffstat(&self) -> Self::Stat

impl Rv<f64> for Gaussian

fn ln_f(&self, x: &f64) -> f64

Un-normalized probability function

fn ln_normalizer(&self) -> f64

The log of the constant term in the PDF/PMF. Should not be a function of any of the parameters.

fn draw<R: Rng>(&self, rng: &mut R) -> f64

Single draw from the Rv

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<f64>

Multiple draws of the Rv

fn f(&self, x: &X) -> f64

Un-normalized probability function

fn normalizer(&self) -> f64

The constant term in the PDF/PMF. Should not be a function of any of the parameters.

impl ContinuousDistr<f64> for Gaussian

fn pdf(&self, x: &X) -> f64

The value of the Probability Density Function (PDF) at x

fn ln_pdf(&self, x: &X) -> f64

The value of the log Probability Density Function (PDF) at x

impl Support<f64> for Gaussian

fn contains(&self, x: &f64) -> bool

Returns true if x is in the support of the Rv

impl Cdf<f64> for Gaussian

fn cdf(&self, x: &f64) -> f64

The value of the Cumulative Density Function at x

fn sf(&self, x: &X) -> f64

Survival function, 1 - CDF(x)

impl InverseCdf<f64> for Gaussian

fn invcdf(&self, p: f64) -> f64

The value of the x at the given probability in the CDF

fn quantile(&self, p: f64) -> X

Alias for invcdf

fn interval(&self, p: f64) -> (X, X)

Interval containing p proportion for the probability

impl Mean<f64> for Gaussian

fn mean(&self) -> Option<f64>

Returns None if the mean is undefined

impl Median<f64> for Gaussian

fn median(&self) -> Option<f64>

Returns None if the median is undefined

impl Mode<f64> for Gaussian

fn mode(&self) -> Option<f64>

Returns None if the mode is undefined or is not a single value

impl HasSuffStat<f64> for Gaussian

type Stat = GaussianSuffStat

fn empty_suffstat(&self) -> Self::Stat

impl Rv<Gaussian> for NormalGamma

fn ln_f(&self, x: &Gaussian) -> f64

Un-normalized probability function

fn ln_normalizer(&self) -> f64

The log of the constant term in the PDF/PMF. Should not be a function of any of the parameters.

fn draw<R: Rng>(&self, rng: &mut R) -> Gaussian

Single draw from the Rv

fn f(&self, x: &X) -> f64

Un-normalized probability function

fn normalizer(&self) -> f64

The constant term in the PDF/PMF. Should not be a function of any of the parameters.

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<X>

Multiple draws of the Rv

impl Support<Gaussian> for NormalGamma

fn contains(&self, x: &Gaussian) -> bool

Returns true if x is in the support of the Rv

impl ContinuousDistr<Gaussian> for NormalGamma

fn pdf(&self, x: &X) -> f64

The value of the Probability Density Function (PDF) at x

fn ln_pdf(&self, x: &X) -> f64

The value of the log Probability Density Function (PDF) at x

impl ConjugatePrior<f64, Gaussian> for NormalGamma

type Posterior = Self

fn posterior(&self, x: &DataOrSuffStat<f64, Gaussian>) -> Self

Computes the posterior distribution from the data

fn ln_m(&self, x: &DataOrSuffStat<f64, Gaussian>) -> f64

Log marginal likelihood

fn ln_pp(&self, y: &f64, x: &DataOrSuffStat<f64, Gaussian>) -> f64

Log posterior predictive of y given x

fn m(&self, x: &DataOrSuffStat<X, Fx>) -> f64

Marginal likelihood of x

fn pp(&self, y: &X, x: &DataOrSuffStat<X, Fx>) -> f64

Posterior Predictive distribution