numpy.random.Generator.logseries¶

method

random.Generator.logseries(p, size=None)¶

Draw samples from a logarithmic series distribution.

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

Parameters

pfloat or array_like of floats: Shape parameter for the distribution. Must be in the range (0, 1).
sizeint 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

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

See also

scipy.stats.logser: probability density function, distribution or cumulative density function, etc.

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].

References

1: Buzas, Martin A.; Culver, Stephen J., Understanding regional species diversity through the log series distribution of occurrences: BIODIVERSITY RESEARCH Diversity & Distributions, Volume 5, Number 5, September 1999 , pp. 187-195(9).
2: Fisher, R.A,, A.S. Corbet, and C.B. Williams. 1943. The relation between the number of species and the number of individuals in a random sample of an animal population. Journal of Animal Ecology, 12:42-58.
3: D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994.
4: Wikipedia, “Logarithmic distribution”, https://en.wikipedia.org/wiki/Logarithmic_distribution

Examples

Draw samples from the distribution:

>>> a = .6
>>> s = np.random.default_rng().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()

../../../_images/numpy-random-Generator-logseries-1.png

numpy.random.Generator.lognormal numpy.random.Generator.multinomial