`numpy.random._generator:Generator.logseries`

Signature

def logseries ( p , size = None )

Summary

Draw samples from a logarithmic series distribution.

Extended Summary

Samples are drawn from a log series distribution with specified shape parameter, 0 <= p < 1.

Parameters

p : float or array_like of floats: Shape parameter for the distribution. Must be in the range [0, 1).
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 p is a scalar. Otherwise, np.array(p).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized logarithmic series distribution.

Notes

The probability mass function for the Log Series distribution is

P (k) = \frac{- p ^{k}}{k ln ( 1 - p )},

where p = probability.

The log series distribution is frequently used to represent species richness and occurrence, first proposed by Fisher, Corbet, and Williams in 1943 ^[2]. It may also be used to model the numbers of occupants seen in cars ^[3].

Examples

Draw samples from the distribution:

a = .6
rng = np.random.default_rng()
s = rng.logseries(a, 10000)
import matplotlib.pyplot as plt
bins = np.arange(-.5, max(s) + .5 )
count, bins, _ = plt.hist(s, bins=bins, label='Sample count')

✓

Plot against the distribution:

def logseries(k, p):
    return -p**k/(k*np.log(1-p))
centres = np.arange(1, max(s) + 1)

✓

plt.plot(centres, logseries(centres, a) * s.size, 'r', label='logseries PMF')
plt.legend()

✗

plt.show()

✓

Aliases

numpy.random.Generator.logseries