Struct statrs::distribution::StudentsT [−][src]
pub struct StudentsT { /* fields omitted */ }
Expand description
Implements the Student’s T distribution
Examples
use statrs::distribution::{StudentsT, Continuous}; use statrs::statistics::Distribution; use statrs::prec; let n = StudentsT::new(0.0, 1.0, 2.0).unwrap(); assert_eq!(n.mean().unwrap(), 0.0); assert!(prec::almost_eq(n.pdf(0.0), 0.353553390593274, 1e-15));
Implementations
impl StudentsT
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impl StudentsT
[src]pub fn new(location: f64, scale: f64, freedom: f64) -> Result<StudentsT>
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pub fn new(location: f64, scale: f64, freedom: f64) -> Result<StudentsT>
[src]Constructs a new student’s t-distribution with location location
,
scale scale
,
and freedom
freedom.
Errors
Returns an error if any of location
, scale
, or freedom
are NaN
.
Returns an error if scale <= 0.0
or freedom <= 0.0
Examples
use statrs::distribution::StudentsT; let mut result = StudentsT::new(0.0, 1.0, 2.0); assert!(result.is_ok()); result = StudentsT::new(0.0, 0.0, 0.0); assert!(result.is_err());
pub fn location(&self) -> f64
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pub fn location(&self) -> f64
[src]Returns the location of the student’s t-distribution
Examples
use statrs::distribution::StudentsT; let n = StudentsT::new(0.0, 1.0, 2.0).unwrap(); assert_eq!(n.location(), 0.0);
Trait Implementations
impl Continuous<f64, f64> for StudentsT
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impl Continuous<f64, f64> for StudentsT
[src]fn pdf(&self, x: f64) -> f64
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fn pdf(&self, x: f64) -> f64
[src]Calculates the probability density function for the student’s
t-distribution
at x
Formula
Γ((v + 1) / 2) / (sqrt(vπ) * Γ(v / 2) * σ) * (1 + k^2 / v)^(-1 / 2 * (v + 1))
where k = (x - μ) / σ
, μ
is the location, σ
is the scale, v
is
the freedom,
and Γ
is the gamma function
fn ln_pdf(&self, x: f64) -> f64
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fn ln_pdf(&self, x: f64) -> f64
[src]Calculates the log probability density function for the student’s
t-distribution
at x
Formula
ln(Γ((v + 1) / 2) / (sqrt(vπ) * Γ(v / 2) * σ) * (1 + k^2 / v)^(-1 / 2 * (v + 1)))
where k = (x - μ) / σ
, μ
is the location, σ
is the scale, v
is
the freedom,
and Γ
is the gamma function
impl ContinuousCDF<f64, f64> for StudentsT
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impl ContinuousCDF<f64, f64> for StudentsT
[src]fn cdf(&self, x: f64) -> f64
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fn cdf(&self, x: f64) -> f64
[src]Calculates the cumulative distribution function for the student’s
t-distribution
at x
Formula
if x < μ { (1 / 2) * I(t, v / 2, 1 / 2) } else { 1 - (1 / 2) * I(t, v / 2, 1 / 2) }
where t = v / (v + k^2)
, k = (x - μ) / σ
, μ
is the location,
σ
is the scale, v
is the freedom, and I
is the regularized
incomplete
beta function
fn inverse_cdf(&self, x: f64) -> f64
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fn inverse_cdf(&self, x: f64) -> f64
[src]Calculates the inverse cumulative distribution function for the
Student’s T-distribution at x
impl Distribution<f64> for StudentsT
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impl Distribution<f64> for StudentsT
[src]fn entropy(&self) -> Option<f64>
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fn entropy(&self) -> Option<f64>
[src]Returns the entropy for the student’s t-distribution
Formula
- ln(σ) + (v + 1) / 2 * (ψ((v + 1) / 2) - ψ(v / 2)) + ln(sqrt(v) * B(v / 2, 1 / 2))
where σ
is the scale, v
is the freedom, ψ
is the digamma function, and B
is the
beta function
impl Distribution<f64> for StudentsT
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impl Distribution<f64> for StudentsT
[src]fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> f64
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fn sample<R: Rng + ?Sized>(&self, r: &mut R) -> f64
[src]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,
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fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
R: Rng,
[src]Create an iterator that generates random values of T
, using rng
as
the source of randomness. Read more
impl Copy for StudentsT
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impl StructuralPartialEq for StudentsT
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Auto Trait Implementations
impl RefUnwindSafe for StudentsT
impl Send for StudentsT
impl Sync for StudentsT
impl Unpin for StudentsT
impl UnwindSafe for StudentsT
Blanket Implementations
impl<T> BorrowMut<T> for T where
T: ?Sized,
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impl<T> BorrowMut<T> for T where
T: ?Sized,
[src]pub fn borrow_mut(&mut self) -> &mut T
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pub fn borrow_mut(&mut self) -> &mut T
[src]Mutably borrows from an owned value. Read more
impl<T> Same<T> for T
impl<T> Same<T> for T
type Output = T
type Output = T
Should always be Self
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,
pub fn to_subset(&self) -> Option<SS>
pub fn to_subset(&self) -> Option<SS>
The inverse inclusion map: attempts to construct self
from the equivalent element of its
superset. Read more
pub fn is_in_subset(&self) -> bool
pub fn is_in_subset(&self) -> bool
Checks if self
is actually part of its subset T
(and can be converted to it).
pub fn to_subset_unchecked(&self) -> SS
pub fn to_subset_unchecked(&self) -> SS
Use with care! Same as self.to_subset
but without any property checks. Always succeeds.
pub fn from_subset(element: &SS) -> SP
pub fn from_subset(element: &SS) -> SP
The inclusion map: converts self
to the equivalent element of its superset.
impl<T> ToOwned for T where
T: Clone,
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impl<T> ToOwned for T where
T: Clone,
[src]type Owned = T
type Owned = T
The resulting type after obtaining ownership.
pub fn to_owned(&self) -> T
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pub fn to_owned(&self) -> T
[src]Creates owned data from borrowed data, usually by cloning. Read more
pub fn clone_into(&self, target: &mut T)
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pub fn clone_into(&self, target: &mut T)
[src]🔬 This is a nightly-only experimental API. (toowned_clone_into
)
recently added
Uses borrowed data to replace owned data, usually by cloning. Read more
impl<V, T> VZip<V> for T where
V: MultiLane<T>,
impl<V, T> VZip<V> for T where
V: MultiLane<T>,