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brainpy.math.random.logseries

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brainpy.math.random.logseries#

brainpy.math.random.logseries(p, size=None, key=None)[source]#

Draw samples from a logarithmic series distribution.

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 – Drawn samples from the parameterized logarithmic series distribution.

Return type:

ndarray or scalar

See also

scipy.stats.logser

probability density function, distribution or cumulative density function, etc.

Notes

The probability density 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].

References

Examples

Draw samples from the distribution:

>>> a = .6
>>> s = bm.random.logseries(a, 10000)
>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s)

# plot against distribution

>>> def logseries(k, p):
...     return -p**k/(k*np.log(1-p))
>>> plt.plot(bins, logseries(bins, a)*count.max()/
...          logseries(bins, a).max(), 'r')
>>> plt.show()
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