Draw samples from a Wald, or inverse Gaussian, distribution.
As the scale approaches infinity, the distribution becomes more like a
Gaussian. Some references claim that the Wald is an inverse Gaussian
with mean equal to 1, but this is by no means universal.
The inverse Gaussian distribution was first studied in relationship to
Brownian motion. In 1956 M.C.K. Tweedie used the name inverse Gaussian
because there is an inverse relationship between the time to cover a
unit distance and distance covered in unit time.
mean (float or array_like of floats) – Distribution mean, should be > 0.
scale (float or array_like of floats) – Scale parameter, should be >= 0.
size (int or tuple of ints, optional) – Output 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 mean and scale are both scalars.
Otherwise, np.broadcast(mean, scale).size samples are drawn.
(m, n, k)
m * n * k
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.
out – Drawn samples from the parameterized Wald distribution.
Tensor or scalar
The probability density function for the Wald distribution is
As noted above the inverse Gaussian distribution first arise
from attempts to model Brownian motion. It is also a
competitor to the Weibull for use in reliability modeling and
modeling stock returns and interest rate processes.
Brighton Webs Ltd., Wald Distribution,
Chhikara, Raj S., and Folks, J. Leroy, “The Inverse Gaussian
Distribution: Theory : Methodology, and Applications”, CRC Press,
Wikipedia, “Wald distribution”
Draw values from the distribution and plot the histogram:
>>> import matplotlib.pyplot as plt
>>> import mars.tensor as mt
>>> h = plt.hist(mt.random.wald(3, 2, 100000).execute(), bins=200, normed=True)