Struct InverseGamma

pub struct InverseGamma { /* private fields */ }

Implements the Inverse Gamma distribution

Examples

use statrs::distribution::{InverseGamma, Continuous};
use statrs::statistics::Distribution;
use statrs::prec;

let n = InverseGamma::new(1.1, 0.1).unwrap();
assert!(prec::almost_eq(n.mean().unwrap(), 1.0, 1e-14));
assert_eq!(n.pdf(1.0), 0.07554920138253064);

Implementations

impl InverseGamma

pub fn new(shape: f64, rate: f64) -> Result<InverseGamma>

Constructs a new inverse gamma distribution with a shape (α) of shape and a rate (β) of rate

Errors

Returns an error if shape or rate are NaN. Also returns an error if shape or rate are not in (0, +inf)

Examples

use statrs::distribution::InverseGamma;

let mut result = InverseGamma::new(3.0, 1.0);
assert!(result.is_ok());

result = InverseGamma::new(0.0, 0.0);
assert!(result.is_err());

pub fn shape(&self) -> f64

Returns the shape (α) of the inverse gamma distribution

Examples

use statrs::distribution::InverseGamma;

let n = InverseGamma::new(3.0, 1.0).unwrap();
assert_eq!(n.shape(), 3.0);

pub fn rate(&self) -> f64

Returns the rate (β) of the inverse gamma distribution

Examples

use statrs::distribution::InverseGamma;

let n = InverseGamma::new(3.0, 1.0).unwrap();
assert_eq!(n.rate(), 1.0);

Trait Implementations

impl Clone for InverseGamma

fn clone(&self) -> InverseGamma

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Continuous<f64, f64> for InverseGamma

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

Calculates the probability density function for the inverse gamma distribution at x

Formula

(β^α / Γ(α)) * x^(-α - 1) * e^(-β / x)

where α is the shape, β is the rate, and Γ is the gamma function

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

Calculates the probability density function for the inverse gamma distribution at x

Formula

ln((β^α / Γ(α)) * x^(-α - 1) * e^(-β / x))

where α is the shape, β is the rate, and Γ is the gamma function

impl ContinuousCDF<f64, f64> for InverseGamma

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

Calculates the cumulative distribution function for the inverse gamma distribution at x

Formula

Γ(α, β / x) / Γ(α)

where the numerator is the upper incomplete gamma function, the denominator is the gamma function, α is the shape, and β is the rate

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

Calculates the survival function for the inverse gamma distribution at x

Formula

Γ(α, β / x) / Γ(α)

where the numerator is the lower incomplete gamma function, the denominator is the gamma function, α is the shape, and β is the rate

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 InverseGamma

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

Formats the value using the given formatter.

impl Distribution<f64> for InverseGamma

fn sample<R: Rng + ?Sized>(&self, r: &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 InverseGamma

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

Returns the mean of the inverse distribution

None

If shape <= 1.0

Formula

β / (α - 1)

where α is the shape and β is the rate

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

Returns the variance of the inverse gamma distribution

None

If shape <= 2.0

Formula

β^2 / ((α - 1)^2 * (α - 2))

where α is the shape and β is the rate

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

Returns the entropy of the inverse gamma distribution

Formula

α + ln(β * Γ(α)) - (1 + α) * ψ(α)

where α is the shape, β is the rate, Γ is the gamma function, and ψ is the digamma function

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

Returns the skewness of the inverse gamma distribution

None

If shape <= 3

Formula

4 * sqrt(α - 2) / (α - 3)

where α is the shape

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

Returns the standard deviation, if it exists.

impl Max<f64> for InverseGamma

fn max(&self) -> f64

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

Formula

INF

impl Min<f64> for InverseGamma

fn min(&self) -> f64

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

Formula

0

impl Mode<Option<f64>> for InverseGamma

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

Returns the mode of the inverse gamma distribution

Formula

β / (α + 1)

/// where α is the shape and β is the rate

impl PartialEq for InverseGamma

fn eq(&self, other: &InverseGamma) -> 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 Copy for InverseGamma

impl StructuralPartialEq for InverseGamma