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., |
---|---|
Returns: |
out : ndarray or scalar Drawn samples from the parameterized logarithmic series distribution. |
See also
scipy.stats.logser
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].
[R475478] | 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). |
[R476478] | 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. |
[R477478] | D. J. Hand, F. Daly, D. Lunn, E. Ostrowski, A Handbook of Small Data Sets, CRC Press, 1994. |
[R478478] | Wikipedia, “Logarithmic distribution”, http://en.wikipedia.org/wiki/Logarithmic_distribution |
Draw samples from the distribution:
>>> a = .6 >>> s = np.random.logseries(a, 10000) >>> count, bins, ignored = plt.hist(s)
# plot against distribution
>>> def logseries(k, p): ... return -p**k/(k*log(1-p)) >>> plt.plot(bins, logseries(bins, a)*count.max()/ logseries(bins, a).max(), 'r') >>> plt.show()
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https://docs.scipy.org/doc/numpy-1.14.2/reference/generated/numpy.random.logseries.html