Struct cont_arith_code::distribution::gaussian::Gaussian

pub struct Gaussian {
    pub s0: usize,
    pub s1: i64,
    pub s2: u128,
    pub ddof: u8,
    pub mean: f64,
    pub stdev: f64,
}

Numerically stable Gaussian distribution

Fields

s0: usize

Number of values

s1: i64

Sum of values

s2: u128

Sum of squares

ddof: u8

0 if values are population, 1 if sample

mean: f64

s1 / s0

stdev: f64

sqrt( (s2 - (s1^2)/s0) / s0 - ddof )

Implementations

impl Gaussian

pub fn variance(&self) -> f64

pub fn mle<I>(data: I, ddof: u8) -> Self

where I: Iterator<Item = i64>,

One pass fit (Max Likelihood Estimation) of a Gaussian to given data, given the desired delta-degree-of-freedom (0 if data is the whole population, 1 if data is a sample)

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

PDF of the normal

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

CDF of the normal

pub fn log_cdf(&self, x: f64) -> f64

log-CDF of the normal

pub fn log_pdf(&self, x: f64) -> f64

pub fn log_survival(&self, x: f64) -> f64

Log of the complement of the CDF of the normal

pub fn log_probability(&self, lo: f64, hi: f64) -> f64

Returns a numerically stable log(abs(cdf(hi) - cdf(lo)))

pub fn quantile(&self, cp: f64) -> f64

pub fn q_cdf(&self, q: usize, x: f64) -> usize

Returns the index of the bin from a division of the curve into q subsets of equal probability

pub fn q_quantile(&self, q: usize, i: usize) -> f64

Returns the i’th q’tile of self, i.e. the value at the boundary between the ith and the i+1th bin of equal 1/q probability for this Gaussian. Input i should be between 1 and q-1 for a real value: i=0 will return f64::NEG_INFINITY and i=q will return f64::INFINITY. Call with q*2 and i*2 + 1 to get the middle of the bin above the boundary

pub fn lerp(&self, lo: f64, hi: f64, cp: f64) -> f64

Does a linear interpolation on the area under the curve of the PDF of the gaussian between two points. Does the computation in log-scale so we’re numerically stable in the tails

pub fn definite_integral(&self, lo: f64, hi: f64) -> f64

Definite integral (equiv. to self.cdf(hi) - self.cdf(lo))

pub fn translate(&self, d: f64) -> Gaussian

Translate the distribution to the right (positive) or to the left (negative) by adding a given amount to the mean

pub fn bits(&self, s: Index) -> f64

Count the information (bits) of a given index in the Gaussian, i.e. the log-probability of the +/-0.5 interval around an integer, in base 2

Trait Implementations

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 Debug for Gaussian

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

Formats the value using the given formatter.

impl Model<i64> for Gaussian

fn push(&mut self, s: i64) -> Option<i64>

Push a value into the model and updates its state. Returns a values once it’s been fully described by a series of indexes.

fn next_distr(&mut self) -> Box<dyn UnivariateDistribution>

Get the distribution for the next symbol from the model.

impl PartialEq for Gaussian

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl PartialOrd for Gaussian

fn partial_cmp(&self, other: &Gaussian) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

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

This method tests less than (for self and other) and is used by the < operator.

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

This method tests less than or equal to (for self and other) and is used by the <= operator.

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

This method tests greater than (for self and other) and is used by the > operator.

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

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl UnivariateDistribution for Gaussian

fn truncated(&self) -> Box<dyn TruncatedDistribution>

impl Copy for Gaussian

impl StructuralPartialEq for Gaussian