Draw samples from a logarithmic series distribution.
Samples are drawn from a log series distribution with specified shape parameter, 0 <
- 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 * ksamples are drawn. If size is
None(default), a single value is returned if
pis a scalar. Otherwise,
np.array(p).sizesamples are drawn.
- out : ndarray or scalar
Drawn samples from the parameterized logarithmic series distribution.
- probability density function, distribution or cumulative density function, etc.
The probability mass function for the Log Series distribution is
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 . It may also be used to model the numbers of occupants seen in cars .
 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).  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.  D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994.  Wikipedia, “Logarithmic distribution”, https://en.wikipedia.org/wiki/Logarithmic_distribution
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()