Struct Gumbel 

pub struct Gumbel { /* private fields */ }

Implements the Gumbel distribution, also known as the type-I generalized extreme value distribution.

Examples

use statrs::distribution::{Gumbel, Continuous};
use statrs::{consts::EULER_MASCHERONI, statistics::Distribution};

let n = Gumbel::new(0.0, 1.0).unwrap();
assert_eq!(n.location(), 0.0);
assert_eq!(n.skewness().unwrap(), 1.13955);
assert_eq!(n.pdf(0.0), 0.36787944117144233);

Implementations

impl Gumbel

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

Constructs a new Gumbel distribution with the given location and scale.

Errors

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

Examples

use statrs::distribution::Gumbel;

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

result = Gumbel::new(0.0, -1.0);
assert!(result.is_err());

pub fn location(&self) -> f64

Returns the location of the Gumbel distribution

Examples

use statrs::distribution::Gumbel;

let n = Gumbel::new(0.0, 1.0).unwrap();
assert_eq!(n.location(), 0.0);

pub fn scale(&self) -> f64

Returns the scale of the Gumbel distribution

Examples

use statrs::distribution::Gumbel;

let n = Gumbel::new(0.0, 1.0).unwrap();
assert_eq!(n.scale(), 1.0);

Trait Implementations

impl Clone for Gumbel

fn clone(&self) -> Gumbel

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for Gumbel

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

Calculates the probability density function for the Gumbel distribution at x

Formula

(1/β) * exp(-(x - μ)/β) * exp(-exp(-(x - μ)/β))

where μ is the location, β is the scale

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

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

Formula

ln((1/β) * exp(-(x - μ)/β) * exp(-exp(-(x - μ)/β)))

where μ is the location, β is the scale

impl ContinuousCDF<f64, f64> for Gumbel

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

Calculates the cumulative distribution function for the Gumbel distribution at x

Formula

e^(-e^(-(x - μ) / β))

where μ is the location and β is the scale

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

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

Formula

μ - β ln(-ln(p)) where 0 < p < 1
-INF             where p <= 0
INF              otherwise

where μ is the location and β is the scale

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

Calculates the survival function for the Gumbel distribution at x

Formula

1 - e^(-e^(-(x - μ) / β))

where μ is the location and β is the scale

impl Debug for Gumbel

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

Formats the value using the given formatter.

impl Display for Gumbel

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

Formats the value using the given formatter.

impl Distribution<f64> for Gumbel

Available on crate feature rand only.

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, 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 Gumbel

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

Returns the entropy of the Gumbel distribution

Formula

ln(β) + γ + 1

where β is the scale and γ is the Euler-Mascheroni constant (approx 0.57721)

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

Returns the mean of the Gumbel distribution

Formula

μ + γβ

where μ is the location, β is the scale and γ is the Euler-Mascheroni constant (approx 0.57721)

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

Returns the skewness of the Gumbel distribution

Formula

12 * sqrt(6) * ζ(3) / π^3 ≈ 1.13955

ζ(3) is the Riemann zeta function evaluated at 3 (approx 1.20206) and π is the constant PI (approx 3.14159)

This approximately evaluates to 1.13955

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

Returns the variance of the Gumbel distribution

Formula

(π^2 / 6) * β^2

where β is the scale and π is the constant PI (approx 3.14159)

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

Returns the standard deviation of the Gumbel distribution

Formula

β * π / sqrt(6)

where β is the scale and π is the constant PI (approx 3.14159)

impl Max<f64> for Gumbel

fn max(&self) -> f64

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

Formula

f64::INFINITY

impl Median<f64> for Gumbel

fn median(&self) -> f64

Returns the median of the Gumbel distribution

Formula

μ - β ln(ln(2))

where μ is the location and β is the scale parameter

impl Min<f64> for Gumbel

fn min(&self) -> f64

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

Formula

NEG_INF

impl Mode<f64> for Gumbel

fn mode(&self) -> f64

Returns the mode of the Gumbel distribution

Formula

μ

where μ is the location

impl PartialEq for Gumbel

fn eq(&self, other: &Gumbel) -> 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 Gumbel

impl StructuralPartialEq for Gumbel