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);

Returns the freedom 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.freedom(), 2.0);

Trait Implementations

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Calculates the probability density function for the 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 cumulative distribution function for the student’s t-distribution at x

Formula
ⓘ
if x < μ {
    1 - (1 / 2) * I(t, v / 2, 1 / 2)
} else {
    (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

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 student’s t-distribution

None

If freedom <= 1.0

Formula
ⓘ
μ

where μ is the location

Returns the variance of the student’s t-distribution

None

If freedom <= 2.0

Formula
ⓘ
if v == INF {
    Some(σ^2)
} else if freedom > 2.0 {
    Some(v * σ^2 / (v - 2))
} else {
    None
}

where σ is the scale and v is the freedom

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

Returns the skewness of the student’s t-distribution

None

If x <= 3.0

Formula
ⓘ
0

Returns the standard deviation, if it exists. Read more

Returns the maximum value in the domain of the student’s t-distribution representable by a double precision float

Formula
ⓘ
INF

Returns the median of the student’s t-distribution

Formula
ⓘ
μ

where μ is the location

Returns the minimum value in the domain of the student’s t-distribution representable by a double precision float

Formula
ⓘ
-INF

Returns the mode of the student’s t-distribution

Formula
ⓘ
μ

where μ is the location

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.