Struct statrs::distribution::Binomial

pub struct Binomial { /* private fields */ }

Implements the Binomial distribution

Examples

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

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

Implementations

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 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 Debug for Binomial

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

Formats the value using the given formatter.

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 DiscreteCDF<u64, f64> for Binomial

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

Calculates 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

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved Specialized inverse cdfs should be used whenever possible.

impl Distribution<f64> for Binomial

fn mean(&self) -> Option<f64>

Returns the mean of the binomial distribution

Formula

p * n

fn variance(&self) -> Option<f64>

Returns the variance of the binomial distribution

Formula

n * p * (1 - p)

fn entropy(&self) -> Option<f64>

Returns the entropy of the binomial distribution

Formula

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

fn skewness(&self) -> Option<f64>

Returns the skewness of the binomial distribution

Formula

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

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

impl Distribution<f64> for Binomial

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generate a random value of T, using rng as the source of randomness.

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T>where R: Rng, Self: Sized,

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S>where F: Fn(T) -> S, Self: Sized,

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

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 Median<f64> for Binomial

fn median(&self) -> f64

Returns the median of the binomial distribution

Formula

floor(n * p)

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 Mode<Option<u64>> for Binomial

fn mode(&self) -> Option<u64>

Returns the mode for the binomial distribution

Formula

floor((n + 1) * p)

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: &Rhs) -> bool

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for Binomial

impl StructuralPartialEq for Binomial