Struct statrs::distribution::FisherSnedecor

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

Implements the Fisher-Snedecor distribution also commonly known as the F-distribution

Examples

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

let n = FisherSnedecor::new(3.0, 3.0).unwrap();
assert_eq!(n.mean().unwrap(), 3.0);
assert!(prec::almost_eq(n.pdf(1.0), 0.318309886183790671538, 1e-15));

Implementations

Constructs a new fisher-snedecor distribution with degrees of freedom freedom_1 and freedom_2

Errors

Returns an error if freedom_1 or freedom_2 are NaN. Also returns an error if freedom_1 <= 0.0 or freedom_2 <= 0.0

Examples
use statrs::distribution::FisherSnedecor;

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

result = FisherSnedecor::new(0.0, 0.0);
assert!(result.is_err());

Returns the first degree of freedom for the fisher-snedecor distribution

Examples
use statrs::distribution::FisherSnedecor;

let n = FisherSnedecor::new(2.0, 3.0).unwrap();
assert_eq!(n.freedom_1(), 2.0);

Returns the second degree of freedom for the fisher-snedecor distribution

Examples
use statrs::distribution::FisherSnedecor;

let n = FisherSnedecor::new(2.0, 3.0).unwrap();
assert_eq!(n.freedom_2(), 3.0);

Trait Implementations

Returns a copy of the value. Read more

Performs copy-assignment from source. Read more

Calculates the probability density function for the fisher-snedecor distribution at x

Remarks

Returns NaN if freedom_1, freedom_2 is INF, or x is +INF or -INF

Formula
ⓘ
sqrt(((d1 * x) ^ d1 * d2 ^ d2) / (d1 * x + d2) ^ (d1 + d2)) / (x * β(d1
/ 2, d2 / 2))

where d1 is the first degree of freedom, d2 is the second degree of freedom, and β is the beta function

Calculates the log probability density function for the fisher-snedecor distribution at x

Remarks

Returns NaN if freedom_1, freedom_2 is INF, or x is +INF or -INF

Formula
ⓘ
ln(sqrt(((d1 * x) ^ d1 * d2 ^ d2) / (d1 * x + d2) ^ (d1 + d2)) / (x *
β(d1 / 2, d2 / 2)))

where d1 is the first degree of freedom, d2 is the second degree of freedom, and β is the beta function

Calculates the cumulative distribution function for the fisher-snedecor distribution at x

Formula
ⓘ
I_((d1 * x) / (d1 * x + d2))(d1 / 2, d2 / 2)

where d1 is the first degree of freedom, d2 is the second degree of freedom, and I is the regularized incomplete beta function

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 fisher-snedecor distribution

Panics

If freedom_2 <= 2.0

Remarks

Returns NaN if freedom_2 is INF

Formula
ⓘ
d2 / (d2 - 2)

where d2 is the second degree of freedom

Returns the variance of the fisher-snedecor distribution

Panics

If freedom_2 <= 4.0

Remarks

Returns NaN if freedom_1 or freedom_2 is INF

Formula
ⓘ
(2 * d2^2 * (d1 + d2 - 2)) / (d1 * (d2 - 2)^2 * (d2 - 4))

where d1 is the first degree of freedom and d2 is the second degree of freedom

Returns the skewness of the fisher-snedecor distribution

Panics

If freedom_2 <= 6.0

Remarks

Returns NaN if freedom_1 or freedom_2 is INF

Formula
ⓘ
((2d1 + d2 - 2) * sqrt(8 * (d2 - 4))) / ((d2 - 6) * sqrt(d1 * (d1 + d2
- 2)))

where d1 is the first degree of freedom and d2 is the second degree of freedom

Returns the standard deviation, if it exists. Read more

Returns the entropy, if it exists. Read more

Returns the maximum value in the domain of the fisher-snedecor distribution representable by a double precision float

Formula
ⓘ
INF

Returns the minimum value in the domain of the fisher-snedecor distribution representable by a double precision float

Formula
ⓘ
0

Returns the mode for the fisher-snedecor distribution

Panics

If freedom_1 <= 2.0

Remarks

Returns NaN if freedom_1 or freedom_2 is INF

Formula
ⓘ
((d1 - 2) / d1) * (d2 / (d2 + 2))

where d1 is the first degree of freedom and d2 is the second degree of freedom

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

This method tests for !=.

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

Performance hack: Clone doesn’t get inlined for Copy types in debug mode, so make it inline anyway.

Tests if Self the same as the type T 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.

The resulting type after obtaining ownership.

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

🔬 This is a nightly-only experimental API. (toowned_clone_into)

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.