Struct statrs::distribution::InverseGamma

pub struct InverseGamma { /* fields omitted */ }

Implements the Inverse Gamma distribution

Examples

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

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

Methods

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 Distribution<f64> for InverseGamma

fn sample<R: Rng>(&self, r: &mut R) -> f64

Generate a random sample from an inverse gamma distribution using r as the source of randomness.

Examples

use rand::StdRng;
use statrs::distribution::{InverseGamma, Distribution};

let mut r = rand::StdRng::new().unwrap();
let n = InverseGamma::new(3.0, 1.0).unwrap();
print!("{}", n.sample::<StdRng>(&mut r));

impl Univariate<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

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 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 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 Mean<f64> for InverseGamma

fn mean(&self) -> f64

Returns the mean of the inverse distribution

Panics

If shape <= 1.0

Formula

β / (α - 1)

where α is the shape and β is the rate

impl CheckedMean<f64> for InverseGamma

fn checked_mean(&self) -> Result<f64>

Returns the mean of the inverse distribution

Errors

If shape <= 1.0

Formula

β / (α - 1)

where α is the shape and β is the rate

impl Variance<f64> for InverseGamma

fn variance(&self) -> f64

Returns the variance of the inverse gamma distribution

Panics

If shape <= 2.0

Formula

β^2 / ((α - 1)^2 * (α - 2))

where α is the shape and β is the rate

fn std_dev(&self) -> f64

Returns the standard deviation of the inverse gamma distribution

Panics

If shape <= 2.0

Formula

sqrt(β^2 / ((α - 1)^2 * (α - 2)))

where α is the shape and β is the rate

impl CheckedVariance<f64> for InverseGamma

fn checked_variance(&self) -> Result<f64>

Returns the variance of the inverse gamma distribution

Errors

If shape <= 2.0

Formula

β^2 / ((α - 1)^2 * (α - 2))

where α is the shape and β is the rate

fn checked_std_dev(&self) -> Result<f64>

Returns the standard deviation of the inverse gamma distribution

Errors

If shape <= 2.0

Formula

sqrt(β^2 / ((α - 1)^2 * (α - 2)))

where α is the shape and β is the rate

impl Entropy<f64> for InverseGamma

fn entropy(&self) -> 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

impl Skewness<f64> for InverseGamma

fn skewness(&self) -> f64

Returns the skewness of the inverse gamma distribution

Panics

If shape <= 3

Formula

4 * sqrt(α - 2) / (α - 3)

where α is the shape

impl CheckedSkewness<f64> for InverseGamma

fn checked_skewness(&self) -> Result<f64>

Returns the skewness of the inverse gamma distribution

Errors

If shape <= 3

Formula

4 * sqrt(α - 2) / (α - 3)

where α is the shape

impl Mode<f64> for InverseGamma

fn mode(&self) -> f64

Returns the mode of the inverse gamma distribution

Formula

β / (α + 1)

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

impl Copy for InverseGamma

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 PartialEq<InverseGamma> for InverseGamma

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

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

fn ne(&self, other: &InverseGamma) -> bool

This method tests for !=.

impl Debug for InverseGamma

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

Formats the value using the given formatter.

impl IndependentSample<f64> for InverseGamma

fn ind_sample<R: Rng>(&self, r: &mut R) -> f64

Generate a random independent sample from an inverse gamma distribution using r as the source of randomness. Refer here for implementation details

impl Sample<f64> for InverseGamma

fn sample<R: Rng>(&mut self, r: &mut R) -> f64

Generate a random sample from an inverse gamma distribution using r as the source of randomness. Refer here for implementation details