Struct Weibull 

pub struct Weibull { /* private fields */ }

Weibull distribution with shape k and scale λ: P(X > x) = exp(-(x/λ)^k), as SciPy’s weibull_min(c=k, scale=λ) and R’s dweibull(shape, scale).

Below shape 1 the tail is heavier than exponential (but every moment exists); above 1 it is lighter. Layer moments use the regularized incomplete gamma: with z = (u/λ)^k, E[X^j; X > u] = λ^j Γ(1 + j/k) Q(1 + j/k, z).

use prospicio_prob::{Distribution, Severity, Weibull};

// Shape 1 is the exponential.
let e = Weibull::new(1.0, 2.0).unwrap();
assert!((e.mean() - 2.0).abs() < 1e-14);
assert!((e.stop_loss(3.0) - 2.0 * (-1.5f64).exp()).abs() < 1e-14);

Implementations

impl Weibull

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

Weibull with shape k > 0 and scale λ > 0.

pub fn shape(&self) -> f64

Shape k.

pub fn scale(&self) -> f64

Scale λ.

Trait Implementations

impl Clone for Weibull

fn clone(&self) -> Weibull

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for Weibull

impl Debug for Weibull

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

Formats the value using the given formatter.

impl Distribution for Weibull

fn quantile(&self, p: f64) -> Result<f64>

λ (-ln(1 - p))^(1/k), with ln(1 - p) taken as ln_1p(-p).

fn mean(&self) -> f64

Expected value.

fn variance(&self) -> f64

Variance.

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

P(X <= x).

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

P(X > x). Representations with a direct form override the default 1 - cdf(x), which loses all precision far in the tail.

fn std_dev(&self) -> f64

Standard deviation.

fn sample(&self, rng: &mut StreamRng, n: usize) -> Vec<f64>

n draws from stream rng, by inverse transform unless the family overrides it (crate::Gamma draws by Marsaglia and Tsang).

fn is_parallel_safe(&self) -> bool

Whether the distribution may be evaluated on several threads at once. True for every native family; false for a crate::Custom whose callbacks must stay on the calling thread (an R function), so the parallel simulations run single-threaded when they meet one.

impl From<Weibull> for Dist

fn from(d: Weibull) -> Self

Converts to this type from the input type.

impl PartialEq for Weibull

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

Equality operator ==.

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

Inequality operator !=.

impl Severity for Weibull

fn lev(&self, limit: f64) -> f64

E[min(X, u)] = λ Γ(1 + 1/k) P(1 + 1/k, z) + u e^(-z).

fn stop_loss(&self, retention: f64) -> f64

From the tail, so it does not cancel against the mean.

fn layer(&self, limit: f64, attachment: f64) -> f64

LEV differences below the mean, stop-loss differences above it.

fn layer_second_moment(&self, limit: f64, attachment: f64) -> f64

t_2(a) - t_2(b) - 2a (t_1(a) - t_1(b)) with b = a + limit.

fn layer_variance(&self, limit: f64, attachment: f64) -> f64

Variance of the loss to the layer limit xs attachment.

impl StructuralPartialEq for Weibull