Struct statrs::distribution::Weibull

pub struct Weibull { /* private fields */ }

Implements the Weibull distribution

Examples

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

let n = Weibull::new(10.0, 1.0).unwrap();
assert!(prec::almost_eq(n.mean().unwrap(),
0.95135076986687318362924871772654021925505786260884, 1e-15));
assert_eq!(n.pdf(1.0), 3.6787944117144232159552377016146086744581113103177);

Implementations

impl Weibull

pub fn new(shape: f64, scale: f64) -> Result<Weibull>

Constructs a new weibull distribution with a shape (k) of shape and a scale (λ) of scale

Errors

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

Examples

use statrs::distribution::Weibull;

let mut result = Weibull::new(10.0, 1.0);
assert!(result.is_ok());

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

pub fn shape(&self) -> f64

Returns the shape of the weibull distribution

Examples

use statrs::distribution::Weibull;

let n = Weibull::new(10.0, 1.0).unwrap();
assert_eq!(n.shape(), 10.0);

pub fn scale(&self) -> f64

Returns the scale of the weibull distribution

Examples

use statrs::distribution::Weibull;

let n = Weibull::new(10.0, 1.0).unwrap();
assert_eq!(n.scale(), 1.0);

Trait Implementations

impl Clone for Weibull

fn clone(&self) -> Weibull

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for Weibull

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

Calculates the probability density function for the weibull distribution at x

Formula

(k / λ) * (x / λ)^(k - 1) * e^(-(x / λ)^k)

where k is the shape and λ is the scale

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

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

Formula

ln((k / λ) * (x / λ)^(k - 1) * e^(-(x / λ)^k))

where k is the shape and λ is the scale

impl ContinuousCDF<f64, f64> for Weibull

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

Calculates the cumulative distribution function for the weibull distribution at x

Formula

1 - e^-((x/λ)^k)

where k is the shape and λ is the scale

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 Weibull

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

Formats the value using the given formatter.

impl Distribution<f64> for Weibull

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, 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 Weibull

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

Returns the mean of the weibull distribution

Formula

λΓ(1 + 1 / k)

where k is the shape, λ is the scale, and Γ is the gamma function

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

Returns the variance of the weibull distribution

Formula

λ^2 * (Γ(1 + 2 / k) - Γ(1 + 1 / k)^2)

where k is the shape, λ is the scale, and Γ is the gamma function

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

Returns the entropy of the weibull distribution

Formula

γ(1 - 1 / k) + ln(λ / k) + 1

where k is the shape, λ is the scale, and γ is the Euler-Mascheroni constant

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

Returns the skewness of the weibull distribution

Formula

(Γ(1 + 3 / k) * λ^3 - 3μσ^2 - μ^3) / σ^3

where k is the shape, λ is the scale, and Γ is the gamma function, μ is the mean of the distribution. and σ the standard deviation of the distribution

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

Returns the standard deviation, if it exists.

impl Max<f64> for Weibull

fn max(&self) -> f64

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

Formula

INF

impl Median<f64> for Weibull

fn median(&self) -> f64

Returns the median of the weibull distribution

Formula

λ(ln(2))^(1 / k)

where k is the shape and λ is the scale

impl Min<f64> for Weibull

fn min(&self) -> f64

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

Formula

0

impl Mode<Option<f64>> for Weibull

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

Returns the median of the weibull distribution

Formula

if k == 1 {
    0
} else {
    λ((k - 1) / k)^(1 / k)
}

where k is the shape and λ is the scale

impl PartialEq<Weibull> for Weibull

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

impl StructuralPartialEq for Weibull