Enum BinomialInterval 

pub enum BinomialInterval {
    Wald,
    Wilson,
    AgrestiCoull,
    Jeffreys,
    ClopperPearson,
}

A confidence interval of a binomial proportion $p$ from $k$ successes among $n$ trials, $\hat{p} = k/n$, $z = \Phi^{-1}(1 - \alpha/2)$ (Brown, Cai & DasGupta 2001, with their equations):

• Wald, eq. (1): $\hat{p} \pm z \sqrt{\hat{p}(1 - \hat{p})/n}$, the textbook interval, whose coverage oscillates far below $1 - \alpha$ (a single point at $k = 0$ or $n$);
• Wilson, eq. (4): the score interval (the default of the runner);
• AgrestiCoull, eq. (5): the Wald interval of $\tilde{p} = (k + z^{2}/2)/(n + z^{2})$ with $\tilde{n} = n + z^{2}$, which contains the Wilson interval;
• Jeffreys, eqs. (6)–(8): the $\alpha/2$ and $1 - \alpha/2$ quantiles of $\mathrm{Beta}(k + 1/2, n - k + 1/2)$, 0 at $k = 0$ and 1 at $k = n$;
• ClopperPearson, Sec. 4.2.1: the quantiles of $\mathrm{Beta}(k, n - k + 1)$ and $\mathrm{Beta}(k + 1, n - k)$, the “exact” interval whose coverage never falls below $1 - \alpha$.

The Wald and Agresti–Coull intervals are returned as the paper defines them, not truncated to $[0, 1]$: their expected lengths are those of its Sec. 3.3 (Fig. 8), and truncating them would not change their coverage of $p \in (0, 1)$.

Variants

Wald

The standard interval, eq. (1).

Wilson

The score interval, eq. (4).

AgrestiCoull

The Agresti–Coull interval, eq. (5).

Jeffreys

The equal-tailed Jeffreys interval, eqs. (6)–(8).

ClopperPearson

The Clopper–Pearson interval, Sec. 4.2.1.

Implementations

impl BinomialInterval

pub const ALL: [BinomialInterval; 5]

The five intervals.

pub fn name(self) -> &'static str

The name of the interval: wald, wilson, agresti_coull, jeffreys or clopper_pearson.

Trait Implementations

impl Clone for BinomialInterval

fn clone(&self) -> Self

Returns a duplicate of the value.

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

Performs copy-assignment from source.

impl Copy for BinomialInterval

impl Debug for BinomialInterval

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

Formats the value using the given formatter.

impl Eq for BinomialInterval

impl FromStr for BinomialInterval

fn from_str(s: &str) -> Result<Self>

The interval of a BinomialInterval::name (any case, - for _).

type Err = Error

The associated error which can be returned from parsing.

impl Hash for BinomialInterval

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H)

where H: Hasher, Self: Sized,

Feeds a slice of this type into the given Hasher.

impl PartialEq for BinomialInterval

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

Equality operator ==.

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

Inequality operator !=.

impl StructuralPartialEq for BinomialInterval