`numpy.random._generator:Generator.pareto`

Signature

def pareto ( a , size = None )

Draw samples from a Pareto II (AKA Lomax) distribution with specified shape.

a : float or array_like of floats: Shape of the distribution. Must be positive.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if a is a scalar. Otherwise, np.array(a).size samples are drawn.

The probability density for the Pareto II distribution is

p (x) = \frac{a}{( x + 1 ) ^{a + 1}}, x \geq 0

where $a > 0$ is the shape.

The Pareto II distribution is a shifted and scaled version of the Pareto I distribution, which can be found in scipy.stats.pareto.

Draw samples from the distribution:

a = 3.
rng = np.random.default_rng()
s = rng.pareto(a, 10000)

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Display the histogram of the samples, along with the probability density function:

import matplotlib.pyplot as plt
x = np.linspace(0, 3, 50)
pdf = a / (x+1)**(a+1)

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plt.hist(s, bins=x, density=True, label='histogram')
plt.plot(x, pdf, linewidth=2, color='r', label='pdf')
plt.xlim(x.min(), x.max())
plt.legend()

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plt.show()

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