distributions.Gamma
Gamma distribution implementation with shape (alpha) and scale (beta)
Usage
distributions.Gamma()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 | Calculate the theoretical mean of the distribution. |
| 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__() | Initialize a Gamma distribution. |
| params_from_mean_and_var() | Derive shape (α) and scale (β) parameters from mean and variance. |
| sample() | Generate random samples from the Gamma distribution. |
__init__()
Initialize a Gamma distribution.
Usage
__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
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
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