numpy.random.wald¶

numpy.random.wald(mean,scale,size=None)¶

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

As the scale approaches infinity, the distribution becomes more like aGaussian. Some references claim that the Wald is an inverse Gaussianwith mean equal to 1, but this is by no means universal.

The inverse Gaussian distribution was first studied in relationship toBrownian motion. In 1956 M.C.K. Tweedie used the name inverse Gaussianbecause there is an inverse relationship between the time to cover aunit distance and distance covered in unit time.

Parameters:	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), thenm*n*k samples are drawn. If size isNone (default),a single value is returned ifmean andscale 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;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 arisefrom attempts to model Brownian motion. It is also acompetitor to the Weibull for use in reliability modeling andmodeling stock returns and interest rate processes.

References

[1]	Brighton Webs Ltd., Wald Distribution,http://www.brighton-webs.co.uk/distributions/wald.asp

[2]	Chhikara, Raj S., and Folks, J. Leroy, “The Inverse GaussianDistribution: Theory : Methodology, and Applications”, CRC Press,1988.

[3]	Wikipedia, “Wald distribution”http://en.wikipedia.org/wiki/Wald_distribution

Examples

Draw values from the distribution and plot the histogram:

>>>importmatplotlib.pyplotasplt>>>h=plt.hist(np.random.wald(3,2,100000),bins=200,density=True)>>>plt.show()