# randomgen.mtrand.RandomState.logseries¶

- 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
**p**float or array_like of floatsShape parameter for the distribution. Must be in the range (0, 1).

**size**int or tuple of ints, optionalOutput 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
**out**ndarray or scalarDrawn 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

\[P(k) = \frac{-p^k}{k \ln(1-p)},\]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.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()