Struct statrs::distribution::Triangular

pub struct Triangular { /* private fields */ }

Implements the Triangular distribution

Examples

use statrs::distribution::{Triangular, Continuous};
use statrs::statistics::Distribution;

let n = Triangular::new(0.0, 5.0, 2.5).unwrap();
assert_eq!(n.mean().unwrap(), 7.5 / 3.0);
assert_eq!(n.pdf(2.5), 5.0 / 12.5);

Implementations

impl Triangular

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

Constructs a new triangular distribution with a minimum of min, maximum of max, and a mode of mode.

Errors

Returns an error if min, max, or mode are NaN or ±INF. Returns an error if max < mode, mode < min, or max == min.

Examples

use statrs::distribution::Triangular;

let mut result = Triangular::new(0.0, 5.0, 2.5);
assert!(result.is_ok());

result = Triangular::new(2.5, 1.5, 0.0);
assert!(result.is_err());

Trait Implementations

impl Clone for Triangular

fn clone(&self) -> Triangular

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for Triangular

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

Calculates the probability density function for the triangular distribution at x

Formula

if x < min {
    0
} else if min <= x <= mode {
    2 * (x - min) / ((max - min) * (mode - min))
} else if mode < x <= max {
    2 * (max - x) / ((max - min) * (max - mode))
} else {
    0
}

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

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

Formula

ln( if x < min {
    0
} else if min <= x <= mode {
    2 * (x - min) / ((max - min) * (mode - min))
} else if mode < x <= max {
    2 * (max - x) / ((max - min) * (max - mode))
} else {
    0
} )

impl ContinuousCDF<f64, f64> for Triangular

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

Calculates the cumulative distribution function for the triangular distribution at x

Formula

if x == min {
    0
} if min < x <= mode {
    (x - min)^2 / ((max - min) * (mode - min))
} else if mode < x < max {
    1 - (max - min)^2 / ((max - min) * (max - mode))
} else {
    1
}

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

Calculates the survival function for the triangular distribution at x

Formula

if x == min {
    1
} if min < x <= mode {
    1 - (x - min)^2 / ((max - min) * (mode - min))
} else if mode < x < max {
    (max - min)^2 / ((max - min) * (max - mode))
} else {
    0
}

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 Triangular

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

Formats the value using the given formatter.

impl Distribution<f64> for Triangular

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 Triangular

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

Returns the mean of the triangular distribution

Formula

(min + max + mode) / 3

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

Returns the variance of the triangular distribution

Formula

(min^2 + max^2 + mode^2 - min * max - min * mode - max * mode) / 18

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

Returns the entropy of the triangular distribution

Formula

1 / 2 + ln((max - min) / 2)

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

Returns the skewness of the triangular distribution

Formula

(sqrt(2) * (min + max - 2 * mode) * (2 * min - max - mode) * (min - 2 *
max + mode)) /
( 5 * (min^2 + max^2 + mode^2 - min * max - min * mode - max * mode)^(3
/ 2))

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

Returns the standard deviation, if it exists.

impl Max<f64> for Triangular

fn max(&self) -> f64

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

Remarks

The return value is the same max used to construct the distribution

impl Median<f64> for Triangular

fn median(&self) -> f64

Returns the median of the triangular distribution

Formula

if mode >= (min + max) / 2 {
    min + sqrt((max - min) * (mode - min) / 2)
} else {
    max - sqrt((max - min) * (max - mode) / 2)
}

impl Min<f64> for Triangular

fn min(&self) -> f64

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

Remarks

The return value is the same min used to construct the distribution

impl Mode<Option<f64>> for Triangular

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

Returns the mode of the triangular distribution

Formula

mode

impl PartialEq for Triangular

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

impl StructuralPartialEq for Triangular