Struct probability::prelude::Binomial

pub struct Binomial {
    // some fields omitted
}

A binomial distribution.

Methods

impl Binomial

fn new(n: usize, p: f64) -> Binomial

Create a binomial distribution with n trails and success probability p.

It should hold that p >= 0 and p <= 1.

fn with_failure(n: usize, q: f64) -> Binomial

Create a binomial distribution with n trails and failure probability q.

It should hold that if q >= 0 or q <= 1. This constructor is preferable when q is very small.

fn n(&self) -> usize

Return the number of trials.

fn p(&self) -> f64

Return the success probability.

fn q(&self) -> f64

Return the failure probability.

Trait Implementations

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 Distribution for Binomial

type Value = usize

The type of outcomes.

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

Compute the cumulative distribution function.

The implementation is based on the incomplete beta function.

impl Discrete for Binomial

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

Compute the probability mass function.

For large n, a saddle-point expansion is used for more accurate computation.

References

1. C. Loader, “Fast and Accurate Computation of Binomial Probabilities,” 2000.

impl Entropy for Binomial

fn entropy(&self) -> f64

Compute the differential entropy.

impl Inverse for Binomial

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

Compute the inverse of the cumulative distribution function.

For small n, a simple summation is utilized. For large n and large variances, a normal asymptotic approximation is used. Otherwise, the Newton method is employed.

References

1. S. Moorhead, “Efficient evaluation of the inverse binomial cumulative distribution function where the number of trials is large,” Oxford University, 2013.

impl Kurtosis for Binomial

fn kurtosis(&self) -> f64

Compute the excess kurtosis.

impl Mean for Binomial

fn mean(&self) -> f64

Compute the expected value.

impl Median for Binomial

fn median(&self) -> f64

Compute the median.

impl Modes for Binomial

fn modes(&self) -> Vec<usize>

Compute the modes.

impl Sample for Binomial

fn sample<S>(&self, source: &mut S) -> usize where S: Source

Draw a sample.

impl Skewness for Binomial

fn skewness(&self) -> f64

Compute the skewness.

impl Variance for Binomial

fn variance(&self) -> f64

Compute the variance.

fn deviation(&self) -> f64

Compute the standard deviation.

fn var(&self) -> f64

Compute the variance.

fn sd(&self) -> f64

Compute the standard deviation.