Struct statrs::distribution::StudentsT
source · [−]pub struct StudentsT { /* private fields */ }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
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());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);Returns the scale 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.scale(), 1.0);Trait Implementations
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
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
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
Calculates the inverse cumulative distribution function for the
Student’s T-distribution at x
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
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
Auto Trait Implementations
impl RefUnwindSafe for StudentsT
impl UnwindSafe for StudentsT
Blanket Implementations
Mutably borrows from an owned value. Read more
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.