Struct statrs::distribution::Poisson

pub struct Poisson { /* private fields */ }

Implements the Poisson distribution

Examples

use statrs::distribution::{Poisson, Discrete};
use statrs::statistics::Distribution;
use statrs::prec;

let n = Poisson::new(1.0).unwrap();
assert_eq!(n.mean().unwrap(), 1.0);
assert!(prec::almost_eq(n.pmf(1), 0.367879441171442, 1e-15));

Implementations

impl Poisson

pub fn new(lambda: f64) -> Result<Poisson>

Constructs a new poisson distribution with a rate (λ) of lambda

Errors

Returns an error if lambda is NaN or lambda <= 0.0

Examples

use statrs::distribution::Poisson;

let mut result = Poisson::new(1.0);
assert!(result.is_ok());

result = Poisson::new(0.0);
assert!(result.is_err());

pub fn lambda(&self) -> f64

Returns the rate (λ) of the poisson distribution

Examples

use statrs::distribution::Poisson;

let n = Poisson::new(1.0).unwrap();
assert_eq!(n.lambda(), 1.0);

Trait Implementations

impl Clone for Poisson

fn clone(&self) -> Poisson

Returns a copy of the value.

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

Performs copy-assignment from source.

impl Debug for Poisson

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

Formats the value using the given formatter.

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 DiscreteCDF<u64, f64> for Poisson

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

Calculates the cumulative distribution function for the poisson distribution at x

Formula

P(x + 1, λ)

where λ is the rate and P is the upper regularized gamma function

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

Calculates the survival function for the poisson distribution at x

Formula

P(x + 1, λ)

where λ is the rate and P is the lower regularized gamma function

fn inverse_cdf(&self, p: T) -> K

Due to issues with rounding and floating-point accuracy the default implementation may be ill-behaved Specialized inverse cdfs should be used whenever possible.

impl Distribution<f64> for Poisson

fn sample<R: Rng + ?Sized>(&self, rng: &mut R) -> f64

Generates one sample from the Poisson distribution either by Knuth’s method if lambda < 30.0 or Rejection method PA by A. C. Atkinson from the Journal of the Royal Statistical Society Series C (Applied Statistics) Vol. 28 No. 1. (1979) pp. 29 - 35 otherwise

fn sample_iter<R>(self, rng: R) -> DistIter<Self, R, T> where
    R: Rng, 

Create an iterator that generates random values of T, using rng as the source of randomness.

fn map<F, S>(self, func: F) -> DistMap<Self, F, T, S> where
    F: Fn(T) -> S, 

Create a distribution of values of ‘S’ by mapping the output of Self through the closure F

impl Distribution<f64> for Poisson

fn mean(&self) -> Option<f64>

Returns the mean of the poisson distribution

Formula

λ

where λ is the rate

fn variance(&self) -> Option<f64>

Returns the variance of the poisson distribution

Formula

λ

where λ is the rate

fn entropy(&self) -> Option<f64>

Returns the entropy of the poisson distribution

Formula

(1 / 2) * ln(2πeλ) - 1 / (12λ) - 1 / (24λ^2) - 19 / (360λ^3)

where λ is the rate

fn skewness(&self) -> Option<f64>

Returns the skewness of the poisson distribution

Formula

λ^(-1/2)

where λ is the rate

fn std_dev(&self) -> Option<T>

Returns the standard deviation, if it exists.

impl Max<u64> for Poisson

fn max(&self) -> u64

Returns the maximum value in the domain of the poisson distribution representable by a 64-bit integer

Formula

2^63 - 1

impl Median<f64> for Poisson

fn median(&self) -> f64

Returns the median of the poisson distribution

Formula

floor(λ + 1 / 3 - 0.02 / λ)

where λ is the rate

impl Min<u64> for Poisson

fn min(&self) -> u64

Returns the minimum value in the domain of the poisson distribution representable by a 64-bit integer

Formula

0

impl Mode<Option<u64>> for Poisson

fn mode(&self) -> Option<u64>

Returns the mode of the poisson distribution

Formula

floor(λ)

where λ is the rate

impl PartialEq<Poisson> for Poisson

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

This method tests for self and other values to be equal, and is used by ==.

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

This method tests for !=. The default implementation is almost always sufficient, and should not be overridden without very good reason.

impl Copy for Poisson

impl StructuralPartialEq for Poisson