Add a SoftLaplace distribution

[fritzo]

From the docs:

This distribution corresponds to the log-convex density::

   z = (value - loc) / scale
   log_prob = log(2 / pi) - log(scale) - logaddexp(z, -z)

Like the Laplace density, this density has the heaviest possible tails
(asymptotically) while still being log-convex. Unlike the Laplace
distribution, this distribution is infinitely differentiable everywhere,
and is thus suitable for constructing Laplace approximations.

import torch
import matplotlib.pyplot as plt
import pyro.distributions as dist
x = torch.linspace(-4, 4, 200)
plt.plot(x, dist.Laplace(0, 1).log_prob(x), "k--", label="Laplace")
plt.plot(x, dist.SoftLaplace(0, 1).log_prob(x), "r-", label="SoftLaplace")
plt.legend(loc="best");

Tested

• added to standard tests, including goftests
• added a cdf-vs-icdf test that is now run on all continuous univariate distributions

[fehiepsi]

Make senses to me: logaddexp(z, -z) ~ |z| in the tail and wolfram alpha shows the correct normalization factor.

[fehiepsi]

LGTM! It would be nice to include some gradient tests, which you taught me previously, but let's do it when more distributions need the test.

[fritzo]

Thanks for reviewing @fehiepsi !