Struct statrs::distribution::Erlang
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pub struct Erlang { /* fields omitted */ }
Implements the Erlang distribution which is a special case of the Gamma distribution
Examples
use statrs::distribution::{Erlang, Continuous}; use statrs::statistics::Mean; use statrs::prec; let n = Erlang::new(3, 1.0).unwrap(); assert_eq!(n.mean(), 3.0); assert!(prec::almost_eq(n.pdf(2.0), 0.270670566473225383788, 1e-15));
Methods
impl Erlang
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fn new(shape: u64, rate: f64) -> Result<Erlang>
Constructs a new erlang distribution with a shape (k)
of shape
and a rate (λ) of rate
Errors
Returns an error if shape
or rate
are NaN
.
Also returns an error if shape == 0
or rate <= 0.0
Examples
use statrs::distribution::Erlang; let mut result = Erlang::new(3, 1.0); assert!(result.is_ok()); result = Erlang::new(0, 0.0); assert!(result.is_err());
fn shape(&self) -> u64
Returns the shape (k) of the erlang distribution
Examples
use statrs::distribution::Erlang; let n = Erlang::new(3, 1.0).unwrap(); assert_eq!(n.shape(), 3);
fn rate(&self) -> f64
Returns the rate (λ) of the erlang distribution
Examples
use statrs::distribution::Erlang; let n = Erlang::new(3, 1.0).unwrap(); assert_eq!(n.rate(), 1.0);
Trait Implementations
impl Debug for Erlang
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impl Copy for Erlang
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impl Clone for Erlang
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fn clone(&self) -> Erlang
Returns a copy of the value. Read more
fn clone_from(&mut self, source: &Self)
1.0.0
Performs copy-assignment from source
. Read more
impl PartialEq for Erlang
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fn eq(&self, __arg_0: &Erlang) -> bool
This method tests for self
and other
values to be equal, and is used by ==
. Read more
fn ne(&self, __arg_0: &Erlang) -> bool
This method tests for !=
.
impl Sample<f64> for Erlang
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fn sample<R: Rng>(&mut self, r: &mut R) -> f64
Generate a random sample from a erlang
distribution using r
as the source of randomness.
Refer here for implementation details
impl IndependentSample<f64> for Erlang
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fn ind_sample<R: Rng>(&self, r: &mut R) -> f64
Generate a random independent sample from a erlang
distribution using r
as the source of randomness.
Refer here for implementation details
impl Distribution<f64> for Erlang
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fn sample<R: Rng>(&self, r: &mut R) -> f64
Generate a random sample from a erlang distribution using
r
as the source of randomness.
Examples
use rand::StdRng; use statrs::distribution::{Erlang, Distribution}; let mut r = rand::StdRng::new().unwrap(); let n = Erlang::new(3, 1.0).unwrap(); print!("{}", n.sample::<StdRng>(&mut r));
impl Univariate<f64, f64> for Erlang
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impl Min<f64> for Erlang
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fn min(&self) -> f64
Returns the minimum value in the domain of the erlang distribution representable by a double precision float
Formula
0
impl Max<f64> for Erlang
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fn max(&self) -> f64
Returns the maximum value in the domain of the erlang distribution representable by a double precision float
Formula
INF
impl Mean<f64> for Erlang
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impl Variance<f64> for Erlang
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fn variance(&self) -> f64
Returns the variance of the erlang distribution
Formula
k / λ^2
where α
is the shape and λ
is the rate
fn std_dev(&self) -> f64
Returns the standard deviation of the erlang distribution
Formula
sqrt(k) / λ
where k
is the shape and λ
is the rate
impl Entropy<f64> for Erlang
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fn entropy(&self) -> f64
Returns the entropy of the erlang distribution
Formula
k - ln(λ) + ln(Γ(k)) + (1 - k) * ψ(k)
where k
is the shape, λ
is the rate, Γ
is the gamma function,
and ψ
is the digamma function
impl Skewness<f64> for Erlang
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impl Mode<f64> for Erlang
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impl Continuous<f64, f64> for Erlang
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fn pdf(&self, x: f64) -> f64
Calculates the probability density function for the erlang distribution
at x
Panics
If x <= 0.0
Remarks
Returns NAN
if any of shape
or rate
are INF
or if x
is INF
Formula
(λ^k / Γ(k)) * x^(k - 1) * e^(-λ * x)
where k
is the shape, λ
is the rate, and Γ
is the gamma function