`numpy.random._generator:Generator.wald`

Signature

def wald ( mean , scale , size = None )

Summary

Draw samples from a Wald, or inverse Gaussian, distribution.

Extended Summary

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.

Parameters

mean : float or array_like of floats: Distribution mean, must be > 0.
scale : float or array_like of floats: Scale parameter, must 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.

Returns

out : ndarray or scalar: Drawn samples from the parameterized Wald distribution.

Notes

The probability density function for the Wald distribution is

P (x; m e an, sc a l e) = \frac{sc a l e}{2 π x ^{3}} e^{\frac{- sc a l e ( x - m e an ) ^{2}}{2 \cdot m e a n ^{2} x}}

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.

Examples

Draw values from the distribution and plot the histogram:

import matplotlib.pyplot as plt
rng = np.random.default_rng()
h = plt.hist(rng.wald(3, 2, 100000), bins=200, density=True)
plt.show()

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Aliases

numpy.random.Generator.wald