numpy.random.RandomState.standard_cauchy — NumPy v1.15 Manual (original) (raw)

RandomState. standard_cauchy(size=None)¶

Draw samples from a standard Cauchy distribution with mode = 0.

Also known as the Lorentz distribution.

Notes

The probability density function for the full Cauchy distribution is

P(x; x_0, \gamma) = \frac{1}{\pi \gamma \bigl[ 1+ (\frac{x-x_0}{\gamma})^2 \bigr] }

and the Standard Cauchy distribution just sets x_0=0 and\gamma=1

The Cauchy distribution arises in the solution to the driven harmonic oscillator problem, and also describes spectral line broadening. It also describes the distribution of values at which a line tilted at a random angle will cut the x axis.

When studying hypothesis tests that assume normality, seeing how the tests perform on data from a Cauchy distribution is a good indicator of their sensitivity to a heavy-tailed distribution, since the Cauchy looks very much like a Gaussian distribution, but with heavier tails.

References

Examples

Draw samples and plot the distribution:

s = np.random.standard_cauchy(1000000) s = s[(s>-25) & (s<25)] # truncate distribution so it plots well plt.hist(s, bins=100) plt.show()