Struct Binomial

pub struct Binomial { /* private fields */ }

Binomial distribution: X ~ Bin(n, p)

Implementations

impl Binomial

pub fn new(trials: usize, probability: f64) -> Binomial

New instance of a Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_eq!(binomial.mean(), 2.0);

Panics

Panics if probability is not in $[0, 1]$.

Trait Implementations

impl Default for Binomial

fn default() -> Binomial

Returns the “default value” for a type.

impl Distribution for Binomial

fn cf(&self, t: f64) -> Complex<f64>

Characteristic function of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);
let cf = binomial.cf(1.0);

assert_approx_equal!(cf.re, -0.2014034, 1e-7);
assert_approx_equal!(cf.im, 0.4969347, 1e-7);

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

Probability density function of the Binomial distribution. Note: Identical to the probability mass function.

Examples

let binomial = Binomial::new(5, 0.4);
let pdf = binomial.pdf(3.0);
let pmf = binomial.pmf(3.0);

assert_approx_equal!(pdf, 0.2304000, 1e-7);
assert_approx_equal!(pdf, pmf, 1e-7);

fn pmf(&self, k: f64) -> f64

Probability mass function of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);
let pmf = binomial.pmf(3.0);

assert_approx_equal!(pmf, 0.2304000, 1e-7);

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

Cumulative distribution function of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_approx_equal!(binomial.cdf(3.0), 0.9129600, 1e-7);

fn inv_cdf(&self, p: f64) -> f64

Inverse distribution (quantile) function of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_eq!(binomial.inv_cdf(0.5), 2.0);    

fn mean(&self) -> f64

Mean of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_eq!(binomial.mean(), 2.0);

fn median(&self) -> f64

Median of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_eq!(binomial.median(), 2.0);

fn mode(&self) -> f64

Mode of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_eq!(binomial.mode(), 2.0);

fn variance(&self) -> f64

Variance of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_eq!(binomial.variance(), 1.2);

fn skewness(&self) -> f64

Skewness of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_approx_equal!(binomial.skewness(), 0.1825742, 1e-7);

fn kurtosis(&self) -> f64

Kurtosis of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_approx_equal!(binomial.kurtosis(), -0.3666667, 1e-7);

fn entropy(&self) -> f64

Entropy of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_approx_equal!(binomial.entropy(), 1.510099, 1e-6);

fn mgf(&self, t: f64) -> f64

Moment generating function of the Binomial distribution.

Examples

let binomial = Binomial::new(5, 0.4);

assert_approx_equal!(binomial.mgf(1.0), 13.67659, 1e-5);

fn sample(&self, n: usize) -> Result<Vec<f64>, RustQuantError>

Generates a random sample from a Binomial distribution.

Examples

let binomial = Binomial::new(100, 0.4);
let sample = binomial.sample(100).unwrap();
let mean = sample.iter().sum::<f64>() / sample.len() as f64;

assert_approx_equal!(mean, binomial.mean(), 1.0);