Struct statrs::distribution::FisherSnedecor

pub struct FisherSnedecor { /* fields omitted */ }

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

Examples

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

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

Methods

impl FisherSnedecor

pub fn new(freedom_1: f64, freedom_2: f64) -> Result<FisherSnedecor>

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());

pub fn freedom_1(&self) -> f64

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);

pub fn freedom_2(&self) -> f64

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

impl Distribution<f64> for FisherSnedecor

fn sample<R: Rng>(&self, r: &mut R) -> f64

Generate a random sample from a fisher-snedecor distribution using r as the source of randomness.

Examples

use rand::StdRng;
use statrs::distribution::{FisherSnedecor, Distribution};

let mut r = rand::StdRng::new().unwrap();
let n = FisherSnedecor::new(2.0, 2.0).unwrap();
print!("{}", n.sample::<StdRng>(&mut r));

impl Univariate<f64, f64> for FisherSnedecor

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

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

impl Continuous<f64, f64> for FisherSnedecor

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

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

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

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

impl Min<f64> for FisherSnedecor

fn min(&self) -> f64

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

Formula

0

impl Max<f64> for FisherSnedecor

fn max(&self) -> f64

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

Formula

INF

impl Mean<f64> for FisherSnedecor

fn mean(&self) -> f64

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

impl CheckedMean<f64> for FisherSnedecor

fn checked_mean(&self) -> Result<f64>

Returns the mean of the fisher-snedecor distribution

Errors

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

impl Variance<f64> for FisherSnedecor

fn variance(&self) -> f64

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

fn std_dev(&self) -> f64

Returns the standard deviation of the fisher-snedecor distribution

Panics

If freedom_2 <= 4.0

Remarks

Returns NaN if freedom_1 or freedom_2 is INF

Formula

sqrt((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

impl CheckedVariance<f64> for FisherSnedecor

fn checked_variance(&self) -> Result<f64>

Returns the variance of the fisher-snedecor distribution

Errors

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

fn checked_std_dev(&self) -> Result<f64>

Returns the standard deviation of the fisher-snedecor distribution

Errors

If freedom_2 <= 4.0

Remarks

Returns NaN if freedom_1 or freedom_2 is INF

Formula

sqrt((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

impl Skewness<f64> for FisherSnedecor

fn skewness(&self) -> f64

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

impl CheckedSkewness<f64> for FisherSnedecor

fn checked_skewness(&self) -> Result<f64>

Returns the skewness of the fisher-snedecor distribution

Errors

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

impl Mode<f64> for FisherSnedecor

fn mode(&self) -> f64

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

impl CheckedMode<f64> for FisherSnedecor

fn checked_mode(&self) -> Result<f64>

Returns the mode for the fisher-snedecor distribution

Errors

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

impl Copy for FisherSnedecor

impl Clone for FisherSnedecor

fn clone(&self) -> FisherSnedecor

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl PartialEq<FisherSnedecor> for FisherSnedecor

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

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

fn ne(&self, other: &FisherSnedecor) -> bool

This method tests for !=.

impl Debug for FisherSnedecor

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

Formats the value using the given formatter.

impl IndependentSample<f64> for FisherSnedecor

fn ind_sample<R: Rng>(&self, r: &mut R) -> f64

Generate a random independent sample from a fisher-snedecor distribution using r as the source of randomness. Refer here for implementation details.

impl Sample<f64> for FisherSnedecor

fn sample<R: Rng>(&mut self, r: &mut R) -> f64

Generate a random sample from a fisher-snedecor distribution using r as the source of randomness. Refer here for implementation details.