Struct Triangular 

pub struct Triangular { /* private fields */ }

Triangular distribution with parameters [min, mode, max].

Mathematical Definition

• PDF: piecewise linear, peaking at mode
• CDF: piecewise quadratic
• Mean: (min + mode + max) / 3
• Variance: (a² + b² + c² − ab − ac − bc) / 18

Reference: Johnson, Kotz & Balakrishnan (1995), Continuous Univariate Distributions, Vol. 2, Chapter 26.

Implementations

impl Triangular

pub fn new(min: f64, mode: f64, max: f64) -> Result<Self, DistributionError>

Creates a new triangular distribution.

Errors

Returns Err if min >= max or mode is outside [min, max].

pub fn min(&self) -> f64

pub fn mode(&self) -> f64

pub fn max(&self) -> f64

pub fn mean(&self) -> f64

Mean = (min + mode + max) / 3.

pub fn variance(&self) -> f64

Variance = (a² + b² + c² − ab − ac − bc) / 18.

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

PDF of the triangular distribution.

f(x) = 2(x−a) / ((c−a)(b−a))  for a ≤ x ≤ b
     = 2(c−x) / ((c−a)(c−b))  for b < x ≤ c
     = 0                       otherwise

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

CDF of the triangular distribution.

F(x) = (x−a)² / ((c−a)(b−a))       for a ≤ x ≤ b
     = 1 − (c−x)² / ((c−a)(c−b))   for b < x ≤ c

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

Inverse CDF (quantile function) of the triangular distribution.

F⁻¹(p) = a + √(p·(c−a)·(b−a))                 if p < F(b)
       = c − √((1−p)·(c−a)·(c−b))              if p ≥ F(b)

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

Trait Implementations

impl Clone for Triangular

fn clone(&self) -> Triangular

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Debug for Triangular

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

Formats the value using the given formatter.

impl PartialEq for Triangular

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