Struct LogNormal

pub struct LogNormal<F>
where
    F: Float,
    StandardNormal: Distribution<F>,
{ /* private fields */ }

The log-normal distribution ln N(μ, σ²).

This is the distribution of the random variable X = exp(Y) where Y is normally distributed with mean μ and variance σ². In other words, if X is log-normal distributed, then ln(X) is N(μ, σ²) distributed.

Plot

The following diagram shows the log-normal distribution with various values of μ and σ.

Example

use rand_distr::{LogNormal, Distribution};

// mean 2, standard deviation 3
let log_normal = LogNormal::new(2.0, 3.0).unwrap();
let v = log_normal.sample(&mut rand::rng());
println!("{} is from an ln N(2, 9) distribution", v)

Implementations

impl<F> LogNormal<F>

where F: Float, StandardNormal: Distribution<F>,

pub fn new(mu: F, sigma: F) -> Result<LogNormal<F>, Error>

Construct, from (log-space) mean and standard deviation

Parameters are the “standard” log-space measures (these are the mean and standard deviation of the logarithm of samples):

• mu (μ, unrestricted) is the mean of the underlying distribution
• sigma (σ, must be finite) is the standard deviation of the underlying Normal distribution

pub fn from_mean_cv(mean: F, cv: F) -> Result<LogNormal<F>, Error>

Construct, from (linear-space) mean and coefficient of variation

Parameters are linear-space measures:

• mean (μ > 0) is the (real) mean of the distribution
• coefficient of variation (cv = σ / μ, requiring cv ≥ 0) is a standardized measure of dispersion

As a special exception, μ = 0, cv = 0 is allowed (samples are -inf).

pub fn from_zscore(&self, zscore: F) -> F

Sample from a z-score

This may be useful for generating correlated samples x1 and x2 from two different distributions, as follows.

let mut rng = rand::rng();
let z = StandardNormal.sample(&mut rng);
let x1 = LogNormal::from_mean_cv(3.0, 1.0).unwrap().from_zscore(z);
let x2 = LogNormal::from_mean_cv(2.0, 4.0).unwrap().from_zscore(z);

Trait Implementations

impl<F> Clone for LogNormal<F>

where F: Clone + Float, StandardNormal: Distribution<F>,

fn clone(&self) -> LogNormal<F>

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl<F> Debug for LogNormal<F>

where F: Debug + Float, StandardNormal: Distribution<F>,

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

Formats the value using the given formatter.

impl<'de, F> Deserialize<'de> for LogNormal<F>

where F: Float + Deserialize<'de>, StandardNormal: Distribution<F>,

fn deserialize<__D>( __deserializer: __D, ) -> Result<LogNormal<F>, <__D as Deserializer<'de>>::Error>

where __D: Deserializer<'de>,

Deserialize this value from the given Serde deserializer.

impl<F> Distribution<F> for LogNormal<F>

where F: Float, StandardNormal: Distribution<F>,

fn sample<R>(&self, rng: &mut R) -> F

where R: Rng + ?Sized,

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

fn sample_iter<R>(self, rng: R) -> Iter<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) -> Map<Self, F, T, S>

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

Map sampled values to type S

impl<F> PartialEq for LogNormal<F>

where F: PartialEq + Float, StandardNormal: Distribution<F>,

fn eq(&self, other: &LogNormal<F>) -> bool

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

const 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<F> Serialize for LogNormal<F>

where F: Float + Serialize, StandardNormal: Distribution<F>,

fn serialize<__S>( &self, __serializer: __S, ) -> Result<<__S as Serializer>::Ok, <__S as Serializer>::Error>

where __S: Serializer,

Serialize this value into the given Serde serializer.

impl<F> Copy for LogNormal<F>

where F: Copy + Float, StandardNormal: Distribution<F>,

impl<F> StructuralPartialEq for LogNormal<F>

where F: Float, StandardNormal: Distribution<F>,