wald(self, mean, scale, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.wald.
Some inconsistencies with the Dask version may exist.
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.
New code should use the wald
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
The probability density function for the Wald distribution is
$$P(x;mean,scale) = \sqrt{\frac{scale}{2\pi x^3}}e^\frac{-scale(x-mean)^2}{2\cdotp mean^2x}$$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.
Distribution mean, must be > 0.
Scale parameter, must be > 0.
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.
Drawn samples from the parameterized Wald distribution.
Draw samples from a Wald, or inverse Gaussian, distribution.
Generator.wald
which should be used for new code.
Draw values from the distribution and plot the histogram:
This example is valid syntax, but we were not able to check execution>>> import matplotlib.pyplot as plt # doctest: +SKIPSee :
... h = plt.hist(np.random.wald(3, 2, 100000), bins=200, density=True) # doctest: +SKIP
... plt.show() # doctest: +SKIP
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