# [−][src]Struct statrs::distribution::Erlang

`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`[src]

#### `pub fn new(shape: u64, rate: f64) -> Result<Erlang>`[src]

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());```

#### `pub fn shape(&self) -> u64`[src]

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);```

#### `pub fn rate(&self) -> f64`[src]

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 Univariate<f64, f64> for Erlang`[src]

#### `fn cdf(&self, x: f64) -> f64`[src]

Calculates the cumulative distribution function for the erlang distribution at `x`

# Formula

`γ(k, λx)  (k - 1)!`

where `k` is the shape, `λ` is the rate, and `γ` is the lower incomplete gamma function

### `impl Continuous<f64, f64> for Erlang`[src]

#### `fn pdf(&self, x: f64) -> f64`[src]

Calculates the probability density function for the erlang distribution at `x`

# 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

#### `fn ln_pdf(&self, x: f64) -> f64`[src]

Calculates the log probability density function for the erlang distribution at `x`

# Remarks

Returns `NAN` if any of `shape` or `rate` are `INF` or if `x` is `INF`

# Formula

`ln((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

### `impl Min<f64> for Erlang`[src]

#### `fn min(&self) -> f64`[src]

Returns the minimum value in the domain of the erlang distribution representable by a double precision float

# Formula

`0`

### `impl Max<f64> for Erlang`[src]

#### `fn max(&self) -> f64`[src]

Returns the maximum value in the domain of the erlang distribution representable by a double precision float

# Formula

`INF`

### `impl Mean<f64> for Erlang`[src]

#### `fn mean(&self) -> f64`[src]

Returns the mean of the erlang distribution

# Remarks

Returns `shape` if `rate == f64::INFINITY`. This behavior is borrowed from the Math.NET implementation

# Formula

`k / λ`

where `k` is the shape and `λ` is the rate

### `impl Variance<f64> for Erlang`[src]

#### `fn variance(&self) -> f64`[src]

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`[src]

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`[src]

#### `fn entropy(&self) -> f64`[src]

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`[src]

#### `fn skewness(&self) -> f64`[src]

Returns the skewness of the erlang distribution

# Formula

`2 / sqrt(k)`

where `k` is the shape

### `impl Mode<f64> for Erlang`[src]

#### `fn mode(&self) -> f64`[src]

Returns the mode for the erlang distribution

# Remarks

Returns `shape` if `rate ==f64::INFINITY`. This behavior is borrowed from the Math.NET implementation

# Formula

`(k - 1) / λ`

where `k` is the shape and `λ` is the rate

### `impl Clone for Erlang`[src]

#### `fn clone_from(&mut self, source: &Self)`1.0.0[src]

Performs copy-assignment from `source`. Read more

### `impl Distribution<f64> for Erlang`[src]

#### `fn sample_iter<R>(&'a self, rng: &'a mut R) -> DistIter<'a, Self, R, T> where    R: Rng, `[src]

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

## Blanket Implementations

### `impl<T> ToOwned for T where    T: Clone, `[src]

#### `type Owned = T`

The resulting type after obtaining ownership.

### `impl<T, U> TryFrom<U> for T where    U: Into<T>, `[src]

#### `type Error = Infallible`

The type returned in the event of a conversion error.

### `impl<T, U> TryInto<U> for T where    U: TryFrom<T>, `[src]

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

The type returned in the event of a conversion error.