Struct Weibull 

pub struct Weibull { /* private fields */ }

Weibull distribution with shape parameter β (> 0) and scale parameter η (> 0).

Widely used in reliability engineering and survival analysis.

Mathematical Definition

• PDF: f(t) = (β/η)·(t/η)^(β−1)·exp(−(t/η)^β) for t ≥ 0
• CDF: F(t) = 1 − exp(−(t/η)^β)
• Quantile: t = η·(−ln(1−p))^(1/β)
• Mean: η·Γ(1 + 1/β)
• Variance: η²·[Γ(1 + 2/β) − Γ(1 + 1/β)²]

Special Cases

• β = 1: Exponential distribution with rate 1/η
• β = 2: Rayleigh distribution
• β ≈ 3.6: Approximates a normal distribution

Reference: Weibull (1951), “A Statistical Distribution Function of Wide Applicability”, Journal of Applied Mechanics 18(3), pp. 293–297.

Implementations

impl Weibull

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

Creates a new Weibull distribution with the given shape (β) and scale (η).

Errors

Returns Err if shape ≤ 0, scale ≤ 0, or either is not finite.

pub fn shape(&self) -> f64

Shape parameter β.

pub fn scale(&self) -> f64

Scale parameter η.

pub fn mean(&self) -> f64

Mean = η·Γ(1 + 1/β).

pub fn variance(&self) -> f64

Variance = η²·[Γ(1 + 2/β) − Γ(1 + 1/β)²].

pub fn pdf(&self, t: f64) -> f64

PDF: f(t) = (β/η)·(t/η)^(β−1)·exp(−(t/η)^β) for t ≥ 0.

pub fn cdf(&self, t: f64) -> f64

CDF: F(t) = 1 − exp(−(t/η)^β).

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

Quantile (inverse CDF): t = η·(−ln(1−p))^(1/β).

Returns None if p is outside [0, 1).

pub fn hazard_rate(&self, t: f64) -> f64

Hazard rate (failure rate): λ(t) = (β/η)·(t/η)^(β−1).

• β < 1: Decreasing failure rate (infant mortality)
• β = 1: Constant failure rate (random failures)
• β > 1: Increasing failure rate (wear-out)

pub fn reliability(&self, t: f64) -> f64

Reliability (survival) function: R(t) = 1 − F(t) = exp(−(t/η)^β).

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 Debug for Weibull

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

Formats the value using the given formatter.

impl PartialEq for Weibull

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