Struct Binomial

pub struct Binomial { /* private fields */ }

A binomial distribution.

Implementations

impl Binomial

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

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

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

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

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.

pub fn n(&self) -> usize

Return the number of trials.

pub fn p(&self) -> f64

Return the success probability.

pub fn q(&self) -> f64

Return the failure probability.

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 for Binomial

fn mass(&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 Distribution for Binomial

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

Compute the cumulative distribution function.

The implementation is based on the incomplete beta function.

type Value = usize

The type of outcomes.

impl Entropy for Binomial

fn entropy(&self) -> f64

Compute the differential entropy.

impl Inverse for Binomial

fn inverse(&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, Newton’s 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.

impl Copy for Binomial