numpy.random.logseries¶

numpy.random.
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:  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)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifp
is a scalar. Otherwise,np.array(p).size
samples are drawn.
Returns:  out : ndarray 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 density 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 [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. 187195(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, 12:4258. [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.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*log(1p)) >>> plt.plot(bins, logseries(bins, a)*count.max()/ logseries(bins, a).max(), 'r') >>> plt.show()