Struct statrs::distribution::Normal

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pub struct Normal { /* private fields */ }

Expand description

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

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impl Normal

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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

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impl Clone for Normal

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fn clone(&self) -> Normal

Returns a copy of the value. Read more

1.0.0 · source

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

Performs copy-assignment from source. Read more

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impl Continuous<f64, f64> for Normal

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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

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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

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impl ContinuousCDF<f64, f64> for Normal

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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

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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

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impl Debug for Normal

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

Formats the value using the given formatter. Read more

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impl Distribution<f64> for Normal

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

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

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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. Read more

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

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

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impl Distribution<f64> for Normal

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

Returns the mean of the normal distribution

Remarks

This is the same mean used to construct the distribution

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

Returns the variance of the normal distribution

Formula

σ^2

where σ is the standard deviation

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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

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

Returns the skewness of the normal distribution

Formula

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

Returns the standard deviation, if it exists. Read more

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impl Max<f64> for Normal

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fn max(&self) -> f64

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

Formula

INF

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impl Median<f64> for Normal

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fn median(&self) -> f64

Returns the median of the normal distribution

Formula

μ

where μ is the mean

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impl Min<f64> for Normal

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fn min(&self) -> f64

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

Formula

-INF

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impl Mode<Option<f64>> for Normal

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

Returns the mode of the normal distribution

Formula

μ

where μ is the mean

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impl PartialEq<Normal> for Normal

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

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

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

This method tests for !=.

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impl Copy for Normal

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impl StructuralPartialEq for Normal

Auto Trait Implementations

impl RefUnwindSafe for Normal

impl Send for Normal

impl Sync for Normal

impl Unpin for Normal

impl UnwindSafe for Normal

Blanket Implementations

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impl<T> Any for T where
T: 'static + ?Sized,

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pub fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Borrow<T> for T where
T: ?Sized,

const: unstable · source

pub fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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impl<T> BorrowMut<T> for T where
T: ?Sized,

const: unstable · source

pub fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

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impl<T> From<T> for T

const: unstable · source

pub fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into for T where
U: From<T>,

const: unstable · source

pub fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Same<T> for T

type Output = T

Should always be Self

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impl<T> Scalar for T where
T: Copy + PartialEq<T> + Debug + Any,

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pub fn inlined_clone(&self) -> T

Performance hack: Clone doesn’t get inlined for Copy types in debug mode, so make it inline anyway.

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fn is<T>() -> bool where
T: Scalar,

Tests if Self the same as the type T Read more

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impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,

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pub fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

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pub fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).

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pub fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

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pub fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.

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impl<T> ToOwned for T where
T: Clone,

type Owned = T

The resulting type after obtaining ownership.

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pub fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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pub fn clone_into(&self, target: &mut T)

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

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impl<T, U> TryFrom for T where
U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

pub fn try_from(value: U) -> Result<T, <T as TryFrom>::Error>

Performs the conversion.

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impl<T, U> TryInto for T where
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

pub fn try_into(self) -> Result<U, >::Error>

Performs the conversion.

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impl<V, T> VZip<V> for T where
V: MultiLane<T>,

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Struct statrs::distribution::Normal

Implementations

impl Normal

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

Trait Implementations

impl Clone for Normal

fn clone(&self) -> Normal

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

impl Continuous<f64, f64> for Normal

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

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

impl ContinuousCDF<f64, f64> for Normal

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

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

impl Debug for Normal

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

impl Distribution<f64> for Normal

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

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

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

impl Distribution<f64> for Normal

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

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

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

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

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

impl Max<f64> for Normal

fn max(&self) -> f64

impl Median<f64> for Normal

fn median(&self) -> f64

impl Min<f64> for Normal

fn min(&self) -> f64

impl Mode<Option<f64>> for Normal

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

impl PartialEq<Normal> for Normal

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

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

impl Copy for Normal

impl StructuralPartialEq for Normal

Auto Trait Implementations

impl RefUnwindSafe for Normal

impl Send for Normal

impl Sync for Normal

impl Unpin for Normal

impl UnwindSafe for Normal

Blanket Implementations

impl<T> Any for T where T: 'static + ?Sized,

pub fn type_id(&self) -> TypeId

impl<T> Borrow<T> for T where T: ?Sized,

pub fn borrow(&self) -> &T

impl<T> BorrowMut<T> for T where T: ?Sized,

pub fn borrow_mut(&mut self) -> &mut T

impl<T> From<T> for T

pub fn from(t: T) -> T

impl<T, U> Into<U> for T where U: From<T>,

pub fn into(self) -> U

impl<T> Same<T> for T

type Output = T

impl<T> Scalar for T where T: Copy + PartialEq<T> + Debug + Any,

pub fn inlined_clone(&self) -> T

fn is<T>() -> bool where T: Scalar,

impl<SS, SP> SupersetOf<SS> for SP where SS: SubsetOf<SP>,

pub fn to_subset(&self) -> Option<SS>

pub fn is_in_subset(&self) -> bool

pub fn to_subset_unchecked(&self) -> SS

pub fn from_subset(element: &SS) -> SP

impl<T> ToOwned for T where T: Clone,

type Owned = T

pub fn to_owned(&self) -> T

pub fn clone_into(&self, target: &mut T)

impl<T, U> TryFrom<U> for T where U: Into<T>,

type Error = Infallible

pub fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

impl<T, U> TryInto<U> for T where U: TryFrom<T>,

type Error = <U as TryFrom<T>>::Error

pub fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

impl<V, T> VZip<V> for T where V: MultiLane<T>,

pub fn vzip(self) -> V

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

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

impl<T> Any for T where
T: 'static + ?Sized,

impl<T> Borrow<T> for T where
T: ?Sized,

impl<T> BorrowMut<T> for T where
T: ?Sized,

impl<T, U> Into<U> for T where
U: From<T>,

impl<T> Scalar for T where
T: Copy + PartialEq<T> + Debug + Any,

fn is<T>() -> bool where
T: Scalar,

impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,

impl<T> ToOwned for T where
T: Clone,

impl<T, U> TryFrom<U> for T where
U: Into<T>,

impl<T, U> TryInto<U> for T where
U: TryFrom<T>,

impl<V, T> VZip<V> for T where
V: MultiLane<T>,