Struct statrs::distribution::Binomial

pub struct Binomial { /* fields omitted */ }

Implements the Binomial distribution

Examples

use statrs::distribution::{Binomial, Discrete};
use statrs::statistics::Mean;

let n = Binomial::new(0.5, 5).unwrap();
assert_eq!(n.mean(), 2.5);
assert_eq!(n.pmf(0), 0.03125);
assert_eq!(n.pmf(3), 0.3125);

Methods

impl Binomial

pub fn new(p: f64, n: u64) -> Result<Binomial>

Constructs a new binomial distribution with a given p probability of success of n trials.

Errors

Returns an error if p is NaN, less than 0.0, greater than 1.0, or if n is less than 0

Examples

use statrs::distribution::Binomial;

let mut result = Binomial::new(0.5, 5);
assert!(result.is_ok());

result = Binomial::new(-0.5, 5);
assert!(result.is_err());

pub fn p(&self) -> f64

Returns the probability of success p of the binomial distribution.

Examples

use statrs::distribution::Binomial;

let n = Binomial::new(0.5, 5).unwrap();
assert_eq!(n.p(), 0.5);

pub fn n(&self) -> u64

Returns the number of trials n of the binomial distribution.

Examples

use statrs::distribution::Binomial;

let n = Binomial::new(0.5, 5).unwrap();
assert_eq!(n.n(), 5);

Trait Implementations

impl Distribution<f64> for Binomial

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

Generate a random sample from the binomial distribution using r as the source of randomness where the range of values is [0.0, n].

Examples

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

let mut r = rand::StdRng::new().unwrap();
let n = Binomial::new(0.5, 5).unwrap();
print!("{}", n.sample::<StdRng>(&mut r));

impl Univariate<u64, f64> for Binomial

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

Calulcates the cumulative distribution function for the binomial distribution at x

Formula

I_(1 - p)(n - x, 1 + x)

where I_(x)(a, b) is the regularized incomplete beta function

impl Discrete<u64, f64> for Binomial

fn pmf(&self, x: u64) -> f64

Calculates the probability mass function for the binomial distribution at x

Formula

(n choose k) * p^k * (1 - p)^(n - k)

fn ln_pmf(&self, x: u64) -> f64

Calculates the log probability mass function for the binomial distribution at x

Formula

ln((n choose k) * p^k * (1 - p)^(n - k))

impl Min<u64> for Binomial

fn min(&self) -> u64

Returns the minimum value in the domain of the binomial distribution representable by a 64-bit integer

Formula

0

impl Max<u64> for Binomial

fn max(&self) -> u64

Returns the maximum value in the domain of the binomial distribution representable by a 64-bit integer

Formula

n

impl Mean<f64> for Binomial

fn mean(&self) -> f64

Returns the mean of the binomial distribution

Formula

p * n

impl Variance<f64> for Binomial

fn variance(&self) -> f64

Returns the variance of the binomial distribution

Formula

n * p * (1 - p)

fn std_dev(&self) -> f64

Returns the standard deviation of the binomial distribution

Formula

sqrt(n * p * (1 - p))

impl Entropy<f64> for Binomial

fn entropy(&self) -> f64

Returns the entropy of the binomial distribution

Formula

(1 / 2) * ln (2 * π * e * n * p * (1 - p))

impl Skewness<f64> for Binomial

fn skewness(&self) -> f64

Returns the skewness of the binomial distribution

Formula

(1 - 2p) / sqrt(n * p * (1 - p)))

impl Median<f64> for Binomial

fn median(&self) -> f64

Returns the median of the binomial distribution

Formula

floor(n * p)

impl Mode<u64> for Binomial

fn mode(&self) -> u64

Returns the mode for the binomial distribution

Formula

floor((n + 1) * p)

impl Copy for Binomial

impl Clone for Binomial

fn clone(&self) -> Binomial

Returns a copy of the value.

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

Performs copy-assignment from source.

impl PartialEq<Binomial> for Binomial

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

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

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

This method tests for !=.

impl Debug for Binomial

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

Formats the value using the given formatter.

impl IndependentSample<f64> for Binomial

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

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

Generate a random value.

impl Sample<f64> for Binomial

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

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