Struct statrs::distribution::LogNormal

pub struct LogNormal { /* private fields */ }

Implements the Log-normal distribution

Examples

use statrs::distribution::{LogNormal, Continuous};
use statrs::statistics::Distribution;
use statrs::prec;

let n = LogNormal::new(0.0, 1.0).unwrap();
assert_eq!(n.mean().unwrap(), (0.5f64).exp());
assert!(prec::almost_eq(n.pdf(1.0), 0.3989422804014326779399, 1e-16));

Implementations

impl LogNormal

pub fn new(location: f64, scale: f64) -> Result<LogNormal>

Constructs a new log-normal distribution with a location of location and a scale of scale

Errors

Returns an error if location or scale are NaN. Returns an error if scale <= 0.0

Examples

use statrs::distribution::LogNormal;

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

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

Trait Implementations

impl Clone for LogNormal

fn clone(&self) -> LogNormal

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for LogNormal

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

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

Formula

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

where μ is the location and σ is the scale

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

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

Formula

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

where μ is the location and σ is the scale

impl ContinuousCDF<f64, f64> for LogNormal

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

Calculates the cumulative distribution function for the log-normal distribution at x

Formula

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

where μ is the location, σ is the scale, and erf is the error function

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

Calculates the survival function for the log-normal distribution at x

Formula

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

where μ is the location, σ is the scale, 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, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved. Specialized inverse cdfs should be used whenever possible. Performs a binary search on the domain of cdf to obtain an approximation of F^-1(p) := inf { x | F(x) >= p }. Needless to say, performance may may be lacking.

impl Debug for LogNormal

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

Formats the value using the given formatter.

impl Distribution<f64> for LogNormal

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, 

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, 

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

impl Distribution<f64> for LogNormal

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

Returns the mean of the log-normal distribution

Formula

e^(μ + σ^2 / 2)

where μ is the location and σ is the scale

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

Returns the variance of the log-normal distribution

Formula

(e^(σ^2) - 1) * e^(2μ + σ^2)

where μ is the location and σ is the scale

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

Returns the entropy of the log-normal distribution

Formula

ln(σe^(μ + 1 / 2) * sqrt(2π))

where μ is the location and σ is the scale

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

Returns the skewness of the log-normal distribution

Formula

(e^(σ^2) + 2) * sqrt(e^(σ^2) - 1)

where μ is the location and σ is the scale

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

Returns the standard deviation, if it exists.

impl Max<f64> for LogNormal

fn max(&self) -> f64

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

Formula

INF

impl Median<f64> for LogNormal

fn median(&self) -> f64

Returns the median of the log-normal distribution

Formula

e^μ

where μ is the location

impl Min<f64> for LogNormal

fn min(&self) -> f64

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

Formula

0

impl Mode<Option<f64>> for LogNormal

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

Returns the mode of the log-normal distribution

Formula

e^(μ - σ^2)

where μ is the location and σ is the scale

impl PartialEq<LogNormal> for LogNormal

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

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

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

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

impl Copy for LogNormal

impl StructuralPartialEq for LogNormal