Trait statrs::distribution::Discrete

pub trait Discrete<T, K> {
    fn pmf(&self, x: T) -> K;
    fn ln_pmf(&self, x: T) -> K;
}

The Discrete trait provides an interface for interacting with discrete statistical distributions

Remarks

All methods provided by the Discrete trait are unchecked, meaning they can panic if in an invalid state or encountering invalid input depending on the implementing distribution.

Required methods

fn pmf(&self, x: T) -> K

Returns the probability mass function calculated at x for a given distribution. May panic depending on the implementor.

Examples

use statrs::distribution::{Discrete, Binomial};
use statrs::prec;

let n = Binomial::new(0.5, 10).unwrap();
assert!(prec::almost_eq(n.pmf(5), 0.24609375, 1e-15));

fn ln_pmf(&self, x: T) -> K

Returns the log of the probability mass function calculated at x for a given distribution. May panic depending on the implementor.

Examples

use statrs::distribution::{Discrete, Binomial};
use statrs::prec;

let n = Binomial::new(0.5, 10).unwrap();
assert!(prec::almost_eq(n.ln_pmf(5), (0.24609375f64).ln(), 1e-15));

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Implementors

impl Discrete<i64, f64> for DiscreteUniform

fn pmf(&self, x: i64) -> f64

Calculates the probability mass function for the discrete uniform distribution at x

Remarks

Returns 0.0 if x is not in [min, max]

Formula

1 / (max - min + 1)

fn ln_pmf(&self, x: i64) -> f64

Calculates the log probability mass function for the discrete uniform distribution at x

Remarks

Returns f64::NEG_INFINITY if x is not in [min, max]

Formula

ln(1 / (max - min + 1))

impl Discrete<u64, f64> for Bernoulli

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

Calculates the probability mass function for the bernoulli distribution at x.

Formula

if x == 0 { 1 - p }
else { p }

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

Calculates the log probability mass function for the bernoulli distribution at x.

Formula

else if x == 0 { ln(1 - p) }
else { ln(p) }

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 Discrete<u64, f64> for Categorical

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

Calculates the probability mass function for the categorical distribution at x

Formula

p_x

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

Calculates the log probability mass function for the categorical distribution at x

impl Discrete<u64, f64> for Geometric

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

Calculates the probability mass function for the geometric distribution at x

Formula

(1 - p)^(x - 1) * p

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

Calculates the log probability mass function for the geometric distribution at x

Formula

ln((1 - p)^(x - 1) * p)

impl Discrete<u64, f64> for Hypergeometric

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

Calculates the probability mass function for the hypergeometric distribution at x

Formula

(K choose x) * (N-K choose n-x) / (N choose n)

where N is population, K is successes, and n is draws

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

Calculates the log probability mass function for the hypergeometric distribution at x

Formula

ln((K choose x) * (N-K choose n-x) / (N choose n))

where N is population, K is successes, and n is draws

impl Discrete<u64, f64> for Poisson

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

Calculates the probability mass function for the poisson distribution at x

Formula

(λ^k * e^(-λ)) / x!

where λ is the rate

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

Calculates the log probability mass function for the poisson distribution at x

Formula

ln((λ^k * e^(-λ)) / x!)

where λ is the rate

impl<'a> Discrete<&'a [u64], f64> for Multinomial

fn pmf(&self, x: &[u64]) -> f64

Calculates the probability mass function for the multinomial distribution with the given x’s corresponding to the probabilities for this distribution

Panics

If the elements in x do not sum to n or if the length of x is not equivalent to the length of p

Formula

(n! / x_1!...x_k!) * p_i^x_i for i in 1...k

where n is the number of trials, p_i is the ith probability, x_i is the ith x value, and k is the total number of probabilities

fn ln_pmf(&self, x: &[u64]) -> f64

Calculates the log probability mass function for the multinomial distribution with the given x’s corresponding to the probabilities for this distribution

Panics

If the elements in x do not sum to n or if the length of x is not equivalent to the length of p

Formula

ln((n! / x_1!...x_k!) * p_i^x_i) for i in 1...k

where n is the number of trials, p_i is the ith probability, x_i is the ith x value, and k is the total number of probabilities

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