Struct Normal

pub struct Normal { /* private fields */ }

Implements the Normal distribution

Examples

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

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

Implementations

impl Normal

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

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());

pub fn standard() -> Normal

Constructs a new standard normal distribution with a mean of 0 and a standard deviation of 1.

Examples

use statrs::distribution::Normal;

let mut result = Normal::standard();

Trait Implementations

impl Clone for Normal

fn clone(&self) -> Normal

Returns a duplicate of the value.

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

Performs copy-assignment from source.

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 ContinuousCDF<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

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

Calculates the survival 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

note that this calculates the complement due to flipping the sign of the argument error function with respect to the cdf.

the normal cdf Φ (and internal error function) as the following property:

 Φ(-x) + Φ(x) = 1
 Φ(-x)        = 1 - Φ(x)

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

Calculates the inverse cumulative distribution function for the normal distribution at x. In other languages, such as R, this is known as the the quantile function.

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 Debug for Normal

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

Formats the value using the given formatter.

impl Default for Normal

fn default() -> Self

Returns the standard normal distribution with a mean of 0 and a standard deviation of 1.

impl Display 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, rng: &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, Self: Sized,

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

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>

where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Distribution<f64> for Normal

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

Returns the mean of the normal distribution

Remarks

This is the same mean used to construct the distribution

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

Returns the variance of the normal distribution

Formula

σ^2

where σ is the standard deviation

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

Returns the standard deviation of the normal distribution

Remarks

This is the same standard deviation used to construct the distribution

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

Returns the entropy of the normal distribution

Formula

(1 / 2) * ln(2σ^2 * π * e)

where σ is the standard deviation

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

Returns the skewness of the normal distribution

Formula

0

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

f64::INFINITY

impl Median<f64> for Normal

fn median(&self) -> f64

Returns the median of the normal distribution

Formula

μ

where μ is the mean

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

f64::NEG_INFINITY

impl Mode<Option<f64>> for Normal

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

Returns the mode of the normal distribution

Formula

μ

where μ is the mean

impl PartialEq for Normal

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

Tests for self and other values to be equal, and is used by ==.

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

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

impl Copy for Normal

impl StructuralPartialEq for Normal