Struct rv::dist::Kumaraswamy

pub struct Kumaraswamy { /* fields omitted */ }

Kumaraswamy distribution, Kumaraswamy(α, β) over x in (0, 1).

Examples

The relationship between the CDF and the inverse CDF.

let kuma = Kumaraswamy::new(2.1, 3.4).unwrap();

let x = 0.6_f64;
let p: f64 = kuma.cdf(&x);
let y: f64 = kuma.invcdf(p);

assert::close(x, y, 1E-10);

Kumaraswamy(a, 1) is equivalent to Beta(a, 1) and Kumaraswamy(1, b) is equivalent to Beta(1, b)

let kuma = Kumaraswamy::new(1.0, 3.5).unwrap();
let beta = Beta::new(1.0, 3.5).unwrap();

let xs = rv::misc::linspace(0.1, 0.9, 10);

for x in xs.iter() {
    assert::close(kuma.f(x), beta.f(x), 1E-10);
}

Methods

impl Kumaraswamy

pub fn new(a: f64, b: f64) -> Result<Self, KumaraswamyError>

Create a Beta distribution with even density over (0, 1).

Example

let kuma_good = Kumaraswamy::new(1.0, 1.0);
assert!(kuma_good.is_ok());

// Invalid negative parameter
let kuma_bad  = Kumaraswamy::new(-5.0, 1.0);
assert!(kuma_bad.is_err());

pub fn new_unchecked(a: f64, b: f64) -> Self

Creates a new Kumaraswamy without checking whether the parameters are valid.

pub fn uniform() -> Self

Create a Kumaraswamy distribution with even density over (0, 1).

Example

let kuma = Kumaraswamy::uniform();
assert_eq!(kuma, Kumaraswamy::new(1.0, 1.0).unwrap());

pub fn centered(a: f64) -> Result<Self, KumaraswamyError>

Create a Kumaraswamy distribution with median 0.5

Notes

The distribution will not necessarily be symmetrical about x = 0.5, i.e., for c < 0.5, f(0.5 - c) may not equal f(0.5 + c).

Examples

// Bowl-shaped
let kuma_1 = Kumaraswamy::centered(0.5).unwrap();
let median_1: f64 = kuma_1.median().unwrap();
assert::close(median_1, 0.5, 1E-10);
assert::close(kuma_1.cdf(&0.5), 0.5, 1E-10);
assert::close(kuma_1.b(), 0.5644763825137, 1E-10);

// Cone-shaped
let kuma_2 = Kumaraswamy::centered(2.0).unwrap();
let median_2: f64 = kuma_2.median().unwrap();
assert::close(median_2, 0.5, 1E-10);
assert::close(kuma_2.cdf(&0.5), 0.5, 1E-10);
assert::close(kuma_2.b(), 2.409420839653209, 1E-10);

The PDF will most likely not be symmetrical about 0.5

fn absolute_error(a: f64, b: f64) -> f64 {
    (a - b).abs()
}

let kuma = Kumaraswamy::centered(2.0).unwrap();
assert!(absolute_error(kuma.f(&0.1), kuma.f(&0.9)) > 1E-8);

pub fn a(&self) -> f64

Get the a parameter

Example

let kuma = Kumaraswamy::new(1.0, 5.0).unwrap();
assert_eq!(kuma.a(), 1.0);

pub fn b(&self) -> f64

Get the b parameter

Example

let kuma = Kumaraswamy::new(1.0, 5.0).unwrap();
assert_eq!(kuma.b(), 5.0);

pub fn set_a(&mut self, a: f64)

pub fn set_b(&mut self, b: f64)

Trait Implementations

impl Cdf<f32> for Kumaraswamy

fn cdf(&self, x: &f32) -> f64

The value of the Cumulative Density Function at x

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

Survival function, 1 - CDF(x)

impl Cdf<f64> for Kumaraswamy

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

The value of the Cumulative Density Function at x

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

Survival function, 1 - CDF(x)

impl Clone for Kumaraswamy

fn clone(&self) -> Self

Returns a copy of the value.

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

Performs copy-assignment from source.

impl ContinuousDistr<f32> for Kumaraswamy

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

The value of the Probability Density Function (PDF) at x

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

The value of the log Probability Density Function (PDF) at x

impl ContinuousDistr<f64> for Kumaraswamy

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

The value of the Probability Density Function (PDF) at x

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

The value of the log Probability Density Function (PDF) at x

impl Debug for Kumaraswamy

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

Formats the value using the given formatter.

impl Default for Kumaraswamy

fn default() -> Self

Returns the "default value" for a type.

impl Display for Kumaraswamy

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

Formats the value using the given formatter.

impl Entropy for Kumaraswamy

fn entropy(&self) -> f64

The entropy, H(X)

impl<'_> From<&'_ Kumaraswamy> for String

fn from(kuma: &Kumaraswamy) -> String

Performs the conversion.

impl InverseCdf<f32> for Kumaraswamy

fn invcdf(&self, p: f64) -> f32

The value of the x at the given probability in the CDF

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

Alias for invcdf

fn interval(&self, p: f64) -> (X, X)

Interval containing p proportion for the probability

impl InverseCdf<f64> for Kumaraswamy

fn invcdf(&self, p: f64) -> f64

The value of the x at the given probability in the CDF

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

Alias for invcdf

fn interval(&self, p: f64) -> (X, X)

Interval containing p proportion for the probability

impl Mean<f32> for Kumaraswamy

fn mean(&self) -> Option<f32>

Returns None if the mean is undefined

impl Mean<f64> for Kumaraswamy

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

Returns None if the mean is undefined

impl Median<f32> for Kumaraswamy

fn median(&self) -> Option<f32>

Returns None if the median is undefined

impl Median<f64> for Kumaraswamy

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

Returns None if the median is undefined

impl Mode<f32> for Kumaraswamy

fn mode(&self) -> Option<f32>

Returns None if the mode is undefined or is not a single value

impl Mode<f64> for Kumaraswamy

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

Returns None if the mode is undefined or is not a single value

impl PartialEq<Kumaraswamy> for Kumaraswamy

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

This method tests for self and other values to be equal, and is used by ==.

#[must_use] fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl Rv<f32> for Kumaraswamy

fn ln_f(&self, x: &f32) -> f64

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> f32

Single draw from the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<X>

Multiple draws of the Rv

impl Rv<f64> for Kumaraswamy

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

Probability function

fn draw<R: Rng>(&self, rng: &mut R) -> f64

Single draw from the Rv

fn f(&self, x: &X) -> f64

Probability function

fn sample<R: Rng>(&self, n: usize, rng: &mut R) -> Vec<X>

Multiple draws of the Rv

impl Support<f32> for Kumaraswamy

fn supports(&self, x: &f32) -> bool

Returns true if x is in the support of the Rv

impl Support<f64> for Kumaraswamy

fn supports(&self, x: &f64) -> bool

Returns true if x is in the support of the Rv