.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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• np.random.seed(42) sets the random seed for consistent results.
• size=(2, 3) creates a 2D array with 2 rows and 3 columns of gamma-distributed samples.