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Gamma

statrs::distribution

Struct Gamma 

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pub struct Gamma { /* private fields */ }
Expand description

Implements the Gamma distribution

§Examples

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

let n = Gamma::new(3.0, 1.0).unwrap();
assert_eq!(n.mean().unwrap(), 3.0);
assert!(prec::almost_eq(n.pdf(2.0), 0.270670566473225383788, 1e-15));

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impl Gamma

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

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

§Errors

Returns an error if shape is ‘NaN’ or inf or rate is NaN or inf. Also returns an error if shape <= 0.0 or rate <= 0.0

§Examples
use statrs::distribution::Gamma;

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

result = Gamma::new(0.0, 0.0);
assert!(result.is_err());
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pub fn shape(&self) -> f64

Returns the shape (α) of the gamma distribution

§Examples
use statrs::distribution::Gamma;

let n = Gamma::new(3.0, 1.0).unwrap();
assert_eq!(n.shape(), 3.0);
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pub fn rate(&self) -> f64

Returns the rate (β) of the gamma distribution

§Examples
use statrs::distribution::Gamma;

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

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impl Clone for Gamma

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fn clone(&self) -> Gamma

Returns a duplicate of the value. Read more
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fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source. Read more
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impl Continuous<f64, f64> for Gamma

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

Calculates the probability density function for the gamma distribution at x

§Remarks

Returns NAN if any of shape or rate are f64::INFINITY or if x is f64::INFINITY

§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

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

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

§Remarks

Returns NAN if any of shape or rate are f64::INFINITY or if x is f64::INFINITY

§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

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impl ContinuousCDF<f64, f64> for Gamma

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

Calculates the cumulative distribution function for the gamma distribution at x

§Formula
(1 / Γ(α)) * γ(α, β * x)

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

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

Calculates the survival function for the gamma distribution at x

§Formula
(1 / Γ(α)) * γ(α, β * x)

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

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

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.
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impl Debug for Gamma

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

Formats the value using the given formatter. Read more
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impl Display for Gamma

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

Formats the value using the given formatter. Read more
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impl Distribution<f64> for Gamma

Available on crate feature rand only.
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fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.
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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. Read more
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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 Read more
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impl Distribution<f64> for Gamma

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

Returns the mean of the gamma distribution

§Formula
α / β

where α is the shape and β is the rate

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

Returns the variance of the gamma distribution

§Formula
α / β^2

where α is the shape and β is the rate

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

Returns the entropy of the gamma distribution

§Formula
α - ln(β) + ln(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

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

Returns the skewness of the gamma distribution

§Formula
2 / sqrt(α)

where α is the shape

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

Returns the standard deviation, if it exists. Read more
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impl Max<f64> for Gamma

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fn max(&self) -> f64

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

§Formula
f64::INFINITY
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impl Min<f64> for Gamma

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fn min(&self) -> f64

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

§Formula
0
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impl Mode<Option<f64>> for Gamma

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

Returns the mode for the gamma distribution

§Formula
(α - 1) / β, where α≥1

where α is the shape and β is the rate

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impl PartialEq for Gamma

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

Tests for self and other values to be equal, and is used by ==.
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fn ne(&self, other: &Rhs) -> bool

Tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.
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impl Copy for Gamma

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impl StructuralPartialEq for Gamma

Auto Trait Implementations§

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impl Freeze for Gamma

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impl RefUnwindSafe for Gamma

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impl Send for Gamma

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impl Sync for Gamma

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impl Unpin for Gamma

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impl UnwindSafe for Gamma

Blanket Implementations§

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impl<T> Any for T
where T: 'static + ?Sized,

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fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more
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impl<T> Borrow<T> for T
where T: ?Sized,

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fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more
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impl<T> BorrowMut<T> for T
where T: ?Sized,

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fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more
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impl<T> CloneToUninit for T
where T: Clone,

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unsafe fn clone_to_uninit(&self, dest: *mut u8)

🔬This is a nightly-only experimental API. (clone_to_uninit)
Performs copy-assignment from self to dest. Read more
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impl<T> From<T> for T

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fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into<U> for T
where U: From<T>,

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fn into(self) -> U

Calls U::from(self).

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

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impl<T> Same for T

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type Output = T

Should always be Self
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impl<SS, SP> SupersetOf<SS> for SP
where SS: SubsetOf<SP>,

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fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more
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fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).
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fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.
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fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.
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impl<T> ToOwned for T
where T: Clone,

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type Owned = T

The resulting type after obtaining ownership.
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fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more
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fn clone_into(&self, target: &mut T)

Uses borrowed data to replace owned data, usually by cloning. Read more
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impl<T> ToString for T
where T: Display + ?Sized,

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fn to_string(&self) -> String

Converts the given value to a String. Read more
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impl<T, U> TryFrom<U> for T
where U: Into<T>,

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type Error = Infallible

The type returned in the event of a conversion error.
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fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

Performs the conversion.
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impl<T, U> TryInto<U> for T
where U: TryFrom<T>,

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type Error = <U as TryFrom<T>>::Error

The type returned in the event of a conversion error.
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fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

Performs the conversion.
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impl<V, T> VZip<V> for T
where V: MultiLane<T>,

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fn vzip(self) -> V

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impl<T> Scalar for T
where T: 'static + Clone + PartialEq + Debug,