This is my first attempt at contributing to any sort of open source project, and I can already see that some of the post-commit checks have failed. I will try to dig into those. Also, I was unable to get Sphinx to build a reference to my added function, so I have not been able to verify if the docstring renders properly.
(1) The first paper that I reference presented this distribution as the "discrete Laplace distribution." This is also how the R programming language refers to this distribution. SciPy, however, appears to use a different distribution for what it calls the "discrete Laplacian distribution." Personally, I feel that referring to the version in my PR as the "two-sided geometric distribution" better conveys how it works.
(2) I describe the parameter 'alpha' as the distribution's "rate of decay." I can see, though, that this may be an inaccurate way to describe 'alpha' since it doesn't work exactly like a "rate of decay" in the Physics sense. Perhaps I should have referred to it as the "distribution's constant ratio." Either way, I think the documentation should be clear enough that a user would not confuse 'alpha' with 'p' from the geometric function (caveat: once the distribution moves away from zero, alpha works like 1 - p).