mars.tensor.random.logseries¶
- mars.tensor.random.logseries(p, size=None, chunk_size=None, gpu=None, dtype=None)[源代码]¶
Draw samples from a logarithmic series distribution.
Samples are drawn from a log series distribution with specified shape parameter, 0 <
p
< 1.- 参数
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.chunk_size (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension
gpu (bool, optional) – Allocate the tensor on GPU if True, False as default
dtype (data-type, optional) – Data-type of the returned tensor.
- 返回
out – Drawn samples from the parameterized logarithmic series distribution.
- 返回类型
Tensor or scalar
参见
scipy.stats.logser
probability density function, distribution or cumulative density function, etc.
提示
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].
引用
- 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”, http://en.wikipedia.org/wiki/Logarithmic_distribution
实际案例
Draw samples from the distribution:
>>> import mars.tensor as mt >>> import matplotlib.pyplot as plt
>>> a = .6 >>> s = mt.random.logseries(a, 10000) >>> count, bins, ignored = plt.hist(s.execute())
# plot against distribution
>>> def logseries(k, p): ... return -p**k/(k*mt.log(1-p)) >>> plt.plot(bins, (logseries(bins, a)*count.max()/ ... logseries(bins, a).max()).execute(), 'r') >>> plt.show()