## distributions.Gamma


Gamma distribution implementation with shape (alpha) and scale (beta)


Usage

``` python
distributions.Gamma(
    alpha,
    beta,
    location=0.0,
    random_seed=None,
)
```


parameters.

This class conforms to the Distribution protocol and provides methods to: - Calculate theoretical mean and variance - Derive parameters from specified mean/variance - Generate samples from the distribution


## Attributes

| Name | Description |
|----|----|
| [mean](#mean) | Calculate the theoretical mean of the distribution. |
| [variance](#variance) | Calculate the theoretical variance of the distribution. |

------------------------------------------------------------------------


#### mean


Calculate the theoretical mean of the distribution.


`mean: float`


------------------------------------------------------------------------


#### variance


Calculate the theoretical variance of the distribution.


`variance: float`


## Methods

| Name | Description |
|----|----|
| [__init__()](#__init__) | Initialize a Gamma distribution. |
| [params_from_mean_and_var()](#params_from_mean_and_var) | Derive shape (α) and scale (β) parameters from mean and variance. |
| [sample()](#sample) | Generate random samples from the Gamma distribution. |

------------------------------------------------------------------------


#### \_\_init\_\_()


Initialize a Gamma distribution.


Usage

``` python
__init__(alpha, beta, location=0.0, random_seed=None)
```


##### Parameters


`alpha: float`  
Shape parameter. Must be \> 0.

`beta: float`  
Scale parameter. Must be \> 0.

`location: float = ``0.0`  
Offset value added to all samples.

`random_seed: Optional[Union[int, SeedSequence]] = None`  
A random seed or SeedSequence to reproduce samples. If None, a unique sample sequence is generated.


##### Raises


`ValueError`  
If alpha or beta or location are not positive.


------------------------------------------------------------------------


#### params_from_mean_and_var()


Derive shape (α) and scale (β) parameters from mean and variance.


Usage

``` python
params_from_mean_and_var(mean, var)
```


##### Parameters


`mean: float`  
Target mean value (μ)

`var: float`  
Target variance value (σ²)


##### Returns


`Tuple[float, float]`  
(alpha, beta) parameters


##### Notes

Uses formulae: - α = μ²/σ² - β = σ²/μ

------------------------------------------------------------------------


#### sample()


Generate random samples from the Gamma distribution.


Usage

``` python
sample(size=None)
```


##### Parameters


`size: Optional[Union[int, Tuple[int, …]]] = None`  
Output shape:

- None returns single sample as float
- int returns 1D array
- tuple returns nD array


##### Returns


`Union[float, NDArray[np.float64]]`  
Samples with specified shape, plus location offset