mars.tensor.random.exponential#
- mars.tensor.random.exponential(scale=1.0, size=None, chunk_size=None, gpu=None, dtype=None)[source]#
Draw samples from an exponential distribution.
Its probability density function is
\[f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),\]for
x > 0
and 0 elsewhere. \(\beta\) is the scale parameter, which is the inverse of the rate parameter \(\lambda = 1/\beta\). The rate parameter is an alternative, widely used parameterization of the exponential distribution 3.The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms 1, or the time between page requests to Wikipedia 2.
- Parameters
scale (float or array_like of floats) – The scale parameter, \(\beta = 1/\lambda\).
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 ifscale
is a scalar. Otherwise,np.array(scale).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.
- Returns
out – Drawn samples from the parameterized exponential distribution.
- Return type
Tensor or scalar
References
- 1
Peyton Z. Peebles Jr., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.
- 2
Wikipedia, “Poisson process”, http://en.wikipedia.org/wiki/Poisson_process
- 3
Wikipedia, “Exponential distribution”, http://en.wikipedia.org/wiki/Exponential_distribution