method
RandomState.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: |
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Returns: |
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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].
[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 |
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*np.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-1.17.0/reference/random/generated/numpy.random.mtrand.RandomState.logseries.html