Struct rv::dist::Kumaraswamy

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pub struct Kumaraswamy { /* private fields */ }

Expand description

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);
}

Implementations§

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impl Kumaraswamy

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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());

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

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

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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());

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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);

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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);

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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);

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pub fn set_a(&mut self, a: f64) -> Result<(), KumaraswamyError>

Set the value of the a parameter

§Example

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

kuma.set_a(2.3).unwrap();
assert_eq!(kuma.a(), 2.3);

Will error for invalid values

assert!(kuma.set_a(2.3).is_ok());
assert!(kuma.set_a(0.0).is_err());
assert!(kuma.set_a(std::f64::INFINITY).is_err());
assert!(kuma.set_a(std::f64::NEG_INFINITY).is_err());
assert!(kuma.set_a(std::f64::NAN).is_err());

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

Set the value of the a parameter without input validation

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pub fn set_b(&mut self, b: f64) -> Result<(), KumaraswamyError>

Set the value of the b parameter

§Example

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

kuma.set_b(2.3).unwrap();
assert_eq!(kuma.b(), 2.3);

Will error for invalid values

assert!(kuma.set_b(2.3).is_ok());
assert!(kuma.set_b(0.0).is_err());
assert!(kuma.set_b(std::f64::INFINITY).is_err());
assert!(kuma.set_b(std::f64::NEG_INFINITY).is_err());
assert!(kuma.set_b(std::f64::NAN).is_err());

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