Struct statrs::distribution::InverseGamma

source · [−]
pub struct InverseGamma { /* private fields */ }
Expand description

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

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());

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);

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

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

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

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

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

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

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. Read more

Formats the value using the given formatter. Read more

Generate a random value of T, using rng as the source of randomness.

Create an iterator that generates random values of T, using rng as the source of randomness. Read more

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F Read more

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

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

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

Returns the skewness of the inverse gamma distribution

None

If shape <= 3

Formula
ⓘ
4 * sqrt(α - 2) / (α - 3)

where α is the shape

Returns the standard deviation, if it exists. Read more

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

Formula
ⓘ
INF

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

Formula
ⓘ
0

Returns the mode of the inverse gamma distribution

Formula
ⓘ
β / (α + 1)

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

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason. Read more

Auto Trait Implementations

Blanket Implementations

Gets the TypeId of self. Read more

Immutably borrows from an owned value. Read more

Mutably borrows from an owned value. Read more

Returns the argument unchanged.

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

Should always be Self

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

Checks if self is actually part of its subset T (and can be converted to it).

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

The inclusion map: converts self to the equivalent element of its superset.

The resulting type after obtaining ownership.

Creates owned data from borrowed data, usually by cloning. Read more

Uses borrowed data to replace owned data, usually by cloning. Read more

The type returned in the event of a conversion error.

Performs the conversion.

The type returned in the event of a conversion error.

Performs the conversion.