Struct statrs::distribution::Poisson

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pub struct Poisson { /* private fields */ }

Expand description

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

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impl Poisson

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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

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

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impl Clone for Poisson

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fn clone(&self) -> Poisson

Returns a copy of the value. Read more

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

Performs copy-assignment from source. Read more

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impl Debug for Poisson

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

Formats the value using the given formatter. Read more

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impl Discrete<u64, f64> for Poisson

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

Calculates the probability mass function for the poisson distribution at x

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

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

impl DiscreteCDF<u64, f64> for Poisson

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

Calculates the cumulative distribution function for the poisson distribution at x

Formula

1 - P(x + 1, λ)

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

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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. Read more

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impl Distribution<f64> for Poisson

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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

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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. Read more

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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 Read more

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impl Distribution<f64> for Poisson

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

Returns the mean of the poisson distribution

Formula

λ

where λ is the rate

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

Returns the variance of the poisson distribution

Formula

λ

where λ is the rate

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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

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

Returns the skewness of the poisson distribution

Formula

λ^(-1/2)

where λ is the rate

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

Returns the standard deviation, if it exists. Read more

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impl Max<u64> for Poisson

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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

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impl Median<f64> for Poisson

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fn median(&self) -> f64

Returns the median of the poisson distribution

Formula

floor(λ + 1 / 3 - 0.02 / λ)

where λ is the rate

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impl Min<u64> for Poisson

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fn min(&self) -> u64

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

Formula

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impl Mode<Option<u64>> for Poisson

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

Returns the mode of the poisson distribution

Formula

floor(λ)

where λ is the rate

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impl PartialEq<Poisson> for Poisson

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

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

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

This method tests for !=.

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impl Copy for Poisson

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impl StructuralPartialEq for Poisson

Auto Trait Implementations

impl RefUnwindSafe for Poisson

impl Send for Poisson

impl Sync for Poisson

impl Unpin for Poisson

impl UnwindSafe for Poisson

Blanket Implementations

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impl<T> Any for T where
T: 'static + ?Sized,

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pub fn type_id(&self) -> TypeId

Gets the TypeId of self. Read more

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impl<T> Borrow<T> for T where
T: ?Sized,

const: unstable · source

pub fn borrow(&self) -> &T

Immutably borrows from an owned value. Read more

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impl<T> BorrowMut<T> for T where
T: ?Sized,

const: unstable · source

pub fn borrow_mut(&mut self) -> &mut T

Mutably borrows from an owned value. Read more

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impl<T> From<T> for T

const: unstable · source

pub fn from(t: T) -> T

Returns the argument unchanged.

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impl<T, U> Into for T where
U: From<T>,

const: unstable · source

pub fn into(self) -> U

Calls U::from(self).

That is, this conversion is whatever the implementation of From<T> for U chooses to do.

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impl<T> Same<T> for T

type Output = T

Should always be Self

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impl<T> Scalar for T where
T: Copy + PartialEq<T> + Debug + Any,

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pub fn inlined_clone(&self) -> T

Performance hack: Clone doesn’t get inlined for Copy types in debug mode, so make it inline anyway.

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fn is<T>() -> bool where
T: Scalar,

Tests if Self the same as the type T Read more

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impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,

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pub fn to_subset(&self) -> Option<SS>

The inverse inclusion map: attempts to construct self from the equivalent element of its superset. Read more

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pub fn is_in_subset(&self) -> bool

Checks if self is actually part of its subset T (and can be converted to it).

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pub fn to_subset_unchecked(&self) -> SS

Use with care! Same as self.to_subset but without any property checks. Always succeeds.

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pub fn from_subset(element: &SS) -> SP

The inclusion map: converts self to the equivalent element of its superset.

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impl<T> ToOwned for T where
T: Clone,

type Owned = T

The resulting type after obtaining ownership.

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pub fn to_owned(&self) -> T

Creates owned data from borrowed data, usually by cloning. Read more

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pub fn clone_into(&self, target: &mut T)

🔬 This is a nightly-only experimental API. (toowned_clone_into)

Uses borrowed data to replace owned data, usually by cloning. Read more

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impl<T, U> TryFrom for T where
U: Into<T>,

type Error = Infallible

The type returned in the event of a conversion error.

const: unstable · source

pub fn try_from(value: U) -> Result<T, <T as TryFrom>::Error>

Performs the conversion.

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impl<T, U> TryInto for T where
U: TryFrom<T>,

type Error = >::Error

The type returned in the event of a conversion error.

const: unstable · source

pub fn try_into(self) -> Result<U, >::Error>

Performs the conversion.

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impl<V, T> VZip<V> for T where
V: MultiLane<T>,

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Struct statrs::distribution::Poisson

Implementations

impl Poisson

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

pub fn lambda(&self) -> f64

Trait Implementations

impl Clone for Poisson

fn clone(&self) -> Poisson

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

impl Debug for Poisson

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

impl Discrete<u64, f64> for Poisson

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

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

impl DiscreteCDF<u64, f64> for Poisson

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

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

impl Distribution<f64> for Poisson

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

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

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

impl Distribution<f64> for Poisson

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

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

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

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

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

impl Max<u64> for Poisson

fn max(&self) -> u64

impl Median<f64> for Poisson

fn median(&self) -> f64

impl Min<u64> for Poisson

fn min(&self) -> u64

impl Mode<Option<u64>> for Poisson

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

impl PartialEq<Poisson> for Poisson

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

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

impl Copy for Poisson

impl StructuralPartialEq for Poisson

Auto Trait Implementations

impl RefUnwindSafe for Poisson

impl Send for Poisson

impl Sync for Poisson

impl Unpin for Poisson

impl UnwindSafe for Poisson

Blanket Implementations

impl<T> Any for T where T: 'static + ?Sized,

pub fn type_id(&self) -> TypeId

impl<T> Borrow<T> for T where T: ?Sized,

pub fn borrow(&self) -> &T

impl<T> BorrowMut<T> for T where T: ?Sized,

pub fn borrow_mut(&mut self) -> &mut T

impl<T> From<T> for T

pub fn from(t: T) -> T

impl<T, U> Into<U> for T where U: From<T>,

pub fn into(self) -> U

impl<T> Same<T> for T

type Output = T

impl<T> Scalar for T where T: Copy + PartialEq<T> + Debug + Any,

pub fn inlined_clone(&self) -> T

fn is<T>() -> bool where T: Scalar,

impl<SS, SP> SupersetOf<SS> for SP where SS: SubsetOf<SP>,

pub fn to_subset(&self) -> Option<SS>

pub fn is_in_subset(&self) -> bool

pub fn to_subset_unchecked(&self) -> SS

pub fn from_subset(element: &SS) -> SP

impl<T> ToOwned for T where T: Clone,

type Owned = T

pub fn to_owned(&self) -> T

pub fn clone_into(&self, target: &mut T)

impl<T, U> TryFrom<U> for T where U: Into<T>,

type Error = Infallible

pub fn try_from(value: U) -> Result<T, <T as TryFrom<U>>::Error>

impl<T, U> TryInto<U> for T where U: TryFrom<T>,

type Error = <U as TryFrom<T>>::Error

pub fn try_into(self) -> Result<U, <U as TryFrom<T>>::Error>

impl<V, T> VZip<V> for T where V: MultiLane<T>,

pub fn vzip(self) -> V

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

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

impl<T> Any for T where
T: 'static + ?Sized,

impl<T> Borrow<T> for T where
T: ?Sized,

impl<T> BorrowMut<T> for T where
T: ?Sized,

impl<T, U> Into<U> for T where
U: From<T>,

impl<T> Scalar for T where
T: Copy + PartialEq<T> + Debug + Any,

fn is<T>() -> bool where
T: Scalar,

impl<SS, SP> SupersetOf<SS> for SP where
SS: SubsetOf<SP>,

impl<T> ToOwned for T where
T: Clone,

impl<T, U> TryFrom<U> for T where
U: Into<T>,

impl<T, U> TryInto<U> for T where
U: TryFrom<T>,

impl<V, T> VZip<V> for T where
V: MultiLane<T>,