Struct Normal 

pub struct Normal<F: Float> {
    pub loc: F,
    pub scale: F,
    /* private fields */
}

Normal distribution structure

Fields

loc: F

Mean (location) parameter

scale: F

Standard deviation (scale) parameter

Implementations

impl<F: Float + NumCast + Display> Normal<F>

pub fn new(loc: F, scale: F) -> StatsResult<Self>

Create a new normal distribution with given mean and standard deviation

Arguments

• loc - Mean (location) parameter
• scale - Standard deviation (scale) parameter

Returns

• A new Normal distribution instance

Examples

use scirs2_stats::distributions::normal::Normal;

let norm = Normal::new(0.0f64, 1.0).expect("Operation failed");

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

Calculate the probability density function (PDF) at a given point

Arguments

• x - The point at which to evaluate the PDF

Returns

• The value of the PDF at the given point

Examples

use scirs2_stats::distributions::normal::Normal;

let norm = Normal::new(0.0f64, 1.0).expect("Operation failed");
let pdf_at_zero = norm.pdf(0.0);
assert!((pdf_at_zero - 0.3989423).abs() < 1e-7);

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

Calculate the cumulative distribution function (CDF) at a given point

Arguments

• x - The point at which to evaluate the CDF

Returns

• The value of the CDF at the given point

Examples

use scirs2_stats::distributions::normal::Normal;

let norm = Normal::new(0.0f64, 1.0).expect("Operation failed");
let cdf_at_zero = norm.cdf(0.0);
assert!((cdf_at_zero - 0.5).abs() < 1e-10);

pub fn ppf(&self, p: F) -> StatsResult<F>

Inverse of the cumulative distribution function (quantile function)

Arguments

• p - Probability value (between 0 and 1)

Returns

• The value x such that CDF(x) = p

Examples

use scirs2_stats::distributions::normal::Normal;

let norm = Normal::new(0.0f64, 1.0).expect("Operation failed");
let x = norm.ppf(0.975).expect("Operation failed");
assert!((x - 1.96).abs() < 1e-2);

pub fn rvs(&self, size: usize) -> StatsResult<Array1<F>>

Generate random samples from the distribution

Arguments

• size - Number of samples to generate

Returns

• Vector of random samples

Examples

use scirs2_stats::distributions::normal::Normal;

let norm = Normal::new(0.0f64, 1.0).expect("Operation failed");
let samples = norm.rvs(1000).expect("Operation failed");
assert_eq!(samples.len(), 1000);

Trait Implementations

impl<F: Float + NumCast + Display> ContinuousDistribution<F> for Normal<F>

fn pdf(&self, x: F) -> F

Probability density function (PDF)

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

Cumulative distribution function (CDF)

fn ppf(&self, p: F) -> StatsResult<F>

Percent point function (inverse CDF)

fn pdf_array(&self, x: &ArrayView1<'_, F>) -> Array1<F>

Vectorised PDF: evaluate pdf at every element of x.

fn cdf_array(&self, x: &ArrayView1<'_, F>) -> Array1<F>

Vectorised CDF: evaluate cdf at every element of x.

fn ppf_array(&self, q: &ArrayView1<'_, F>) -> StatsResult<Array1<F>>

Vectorised PPF: evaluate ppf at every element of q.

impl<F: Float + NumCast + Display> Distribution<F> for Normal<F>

fn mean(&self) -> F

Mean (expected value) of the distribution

fn var(&self) -> F

Variance of the distribution

fn std(&self) -> F

Standard deviation of the distribution

fn rvs(&self, size: usize) -> StatsResult<Array1<F>>

Generate random samples from the distribution

fn entropy(&self) -> F

Entropy of the distribution

fn rvs_array(&self, shape: &[usize]) -> StatsResult<ArrayD<F>>

Generate random samples with a user-specified output shape.

impl<F: Float + NumCast + Display> SampleableDistribution<F> for Normal<F>

Implementation of SampleableDistribution for Normal

fn rvs(&self, size: usize) -> StatsResult<Vec<F>>

Generate random samples from the distribution