Struct russell_stat::DistributionGumbel

pub struct DistributionGumbel { /* private fields */ }

Implements the Gumbel distribution

This is a Type I Extreme Value Distribution (largest value)

See: https://en.wikipedia.org/wiki/Gumbel_distribution

Implementations

impl DistributionGumbel

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

Allocates a new instance

Input

• location – characteristic largest value
• scale – measure of dispersion of the largest value

pub fn new_from_mu_sig(mu: f64, sig: f64) -> Result<Self, StrError>

Creates a new Gumbel distribution given mean and standard deviation parameters

Input

• mu – mean μ
• sig – standard deviation σ

Trait Implementations

impl ProbabilityDistribution for DistributionGumbel

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

Evaluates the Probability Density Function (PDF)

use russell_lab::approx_eq;
use russell_stat::*;

fn main() -> Result<(), StrError> {
    let (location, scale) = (2.0, 3.0);
    let dist = DistributionGumbel::new(location, scale)?;
    approx_eq(dist.pdf(1.0), 0.11522236828583457, 1e-15);
    // R:
    //   library(evd)
    //   format(dgumbel(1.0, 2.0, 3.0), digits=17)
    // Mathematica:
    //   N[PDF[GumbelDistribution[-2, 3], -1], 17]
    Ok(())
}

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

Evaluates the Cumulative Distribution Function (CDF)

use russell_lab::approx_eq;
use russell_stat::*;

fn main() -> Result<(), StrError> {
    let (location, scale) = (2.0, 3.0);
    let dist = DistributionGumbel::new(location, scale)?;
    approx_eq(dist.cdf(1.0), 0.24768130366579455, 1e-15);
    // R:
    //   library(evd)
    //   format(pgumbel(1.0, 2.0, 3.0), digits=17)
    // Mathematica:
    //   N[1 - CDF[GumbelDistribution[-2, 3], -1], 17]
    Ok(())
}

fn mean(&self) -> f64

Returns the Mean

use russell_lab::{approx_eq, math::EULER};
use russell_stat::*;

fn main() -> Result<(), StrError> {
    let (location, scale) = (2.0, 3.0);
    let dist = DistributionGumbel::new(location, scale)?;
    approx_eq(dist.mean(), location + EULER * scale, 1e-15);
    // Mathematica: -Mean[GumbelDistribution[-location, scale]]
    Ok(())
}

fn variance(&self) -> f64

Returns the Variance

Examples

use russell_lab::approx_eq;
use russell_stat::*;

fn main() -> Result<(), StrError> {
    let (location, scale) = (2.0, 3.0);
    let dist = DistributionGumbel::new(location, scale)?;
    approx_eq(dist.variance(), 14.804406601634038, 1e-14);
    // Mathematica: N[Variance[GumbelDistribution[-2, 3]], 17]
    Ok(())
}

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

Generates a pseudo-random number belonging to this probability distribution

Examples

use russell_stat::*;

fn main() -> Result<(), StrError> {
    let (location, scale) = (2.0, 3.0);
    let dist = DistributionGumbel::new(location, scale)?;
    let mut rng = get_rng();
    println!("sample = {}", dist.sample(&mut rng));
    Ok(())
}