Python:NumPy .gamma()

The .gamma() function of the NumPy Random module generates random samples from a Gamma distribution, a two-parameter continuous probability distribution commonly used in statistics for modeling positive-valued data. The two parameters are shape and scale .

Syntax

numpy.random.gamma(shape, scale=1.0, size=None)
Parameters:
shape (float or array_like of floats): The shape parameter, denoted as $\kappa$ (or $k$). Must be non-negative. Determines the shape of the distribution.
scale (float or array_like of floats, optional): The scale parameter, denoted as $\theta$. Must be non-negative. Default is 1.0. It stretches or compresses the distribution.
size (int or tuple of ints, optional): The output shape. Specifies the number or shape of random samples to generate. If None (default), a single sample is returned.
Return value:
out (ndarray or scalar): Random samples from the Gamma distribution.

If size is None, returns a single float.
If size is specified, returns a NumPy array of shape size containing the sampled values.
Statistical Properties
Mean: $μ=αθμ=αθ$
Variance: $σ2=αθ2σ2=αθ2$
The probability density formula for the Gamma distribution is:
p(x) = x^{k-1} \frac{e^{-x/\theta}} {\theta^{k}\Gamma(k)’}
$\kappa$ is the shape, $\theta$ is scale, and $\Gamma$ is the Gamma function.
Example
This example generates two reproducible random samples from a Gamma distribution of shape = 2 and scale = 2:
import numpy as np
np.random.seed(15)
result = np.random.gamma(shape=2,scale=2,size=2)
print(result)

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The output for this code will be:
[2.59018924 4.28834638]

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Here:
np.random.seed(15) ensures the output is reproducible across runs.
np.random.gamma() draws two samples from the specified Gamma distribution.
Codebyte Example
This codebyte example generates a 2×3 array of Gamma-distributed random numbers with shape = 5 and scale = 1.5:
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