Struct statrs::distribution::Normal

pub struct Normal { /* fields omitted */ }

Implements the Normal distribution

Examples

use statrs::distribution::{Normal, Continuous};
use statrs::statistics::Mean;

let n = Normal::new(0.0, 1.0).unwrap();
assert_eq!(n.mean(), 0.0);
assert_eq!(n.pdf(1.0), 0.2419707245191433497978);

Methods

impl Normal

pub fn new(mean: f64, std_dev: f64) -> Result<Normal>

Constructs a new normal distribution with a mean of mean and a standard deviation of std_dev

Errors

Returns an error if mean or std_dev are NaN or if std_dev <= 0.0

Examples

use statrs::distribution::Normal;

let mut result = Normal::new(0.0, 1.0);
assert!(result.is_ok());

result = Normal::new(0.0, 0.0);
assert!(result.is_err());

Trait Implementations

impl Univariate<f64, f64> for Normal

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

Calculates the cumulative distribution function for the normal distribution at x

Formula

(1 / 2) * (1 + erf((x - μ) / (σ * sqrt(2))))

where μ is the mean, σ is the standard deviation, and erf is the error function

impl InverseCDF<f64> for Normal

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

Calculates the inverse cumulative distribution function for the normal distribution at x

Panics

If x < 0.0 or x > 1.0

Formula

μ - sqrt(2) * σ * erfc_inv(2x)

where μ is the mean, σ is the standard deviation and erfc_inv is the inverse of the complementary error function

impl CheckedInverseCDF<f64> for Normal

fn checked_inverse_cdf(&self, x: f64) -> Result<f64>

Calculates the inverse cumulative distribution function for the normal distribution at x

Errors

If x < 0.0 or x > 1.0

Formula

μ - sqrt(2) * σ * erfc_inv(2x)

where μ is the mean, σ is the standard deviation and erfc_inv is the inverse of the complementary error function

impl Continuous<f64, f64> for Normal

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

Calculates the probability density function for the normal distribution at x

Formula

(1 / sqrt(2σ^2 * π)) * e^(-(x - μ)^2 / 2σ^2)

where μ is the mean and σ is the standard deviation

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

Calculates the log probability density function for the normal distribution at x

Formula

ln((1 / sqrt(2σ^2 * π)) * e^(-(x - μ)^2 / 2σ^2))

where μ is the mean and σ is the standard deviation

impl Min<f64> for Normal

fn min(&self) -> f64

Returns the minimum value in the domain of the normal distribution representable by a double precision float

Formula

-INF

impl Max<f64> for Normal

fn max(&self) -> f64

Returns the maximum value in the domain of the normal distribution representable by a double precision float

Formula

INF

impl Mean<f64> for Normal

fn mean(&self) -> f64

Returns the mean of the normal distribution

Remarks

This is the same mean used to construct the distribution

impl Variance<f64> for Normal

fn variance(&self) -> f64

Returns the variance of the normal distribution

Formula

σ^2

where σ is the standard deviation

fn std_dev(&self) -> f64

Returns the standard deviation of the normal distribution

Remarks

This is the same standard deviation used to construct the distribution

impl Entropy<f64> for Normal

fn entropy(&self) -> f64

Returns the entropy of the normal distribution

Formula

(1 / 2) * ln(2σ^2 * π * e)

where σ is the standard deviation

impl Skewness<f64> for Normal

fn skewness(&self) -> f64

Returns the skewness of the normal distribution

Formula

0

impl Median<f64> for Normal

fn median(&self) -> f64

Returns the median of the normal distribution

Formula

μ

where μ is the mean

impl Mode<f64> for Normal

fn mode(&self) -> f64

Returns the mode of the normal distribution

Formula

μ

where μ is the mean

impl Clone for Normal

fn clone(&self) -> Normal

Returns a copy of the value.

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

Performs copy-assignment from source.

impl PartialEq<Normal> for Normal

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

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

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

This method tests for !=.

impl Copy for Normal

impl Debug for Normal

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

Formats the value using the given formatter.

impl Distribution<f64> for Normal

fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.