What distribution looks like a uniform distribution with decaying density at the extremes?

Question

I was wondering if there exists a distribution with this general shape:

I want to model something using a prior distribution that is uniform in its interior, and then smoothly (but relatively quickly--hopefully theres a parameter for this) decays to $0$ at the extremes. Does such a distribution, defined on $\mathbb R$, exist?

Answer 1

Perhaps you should look at the "smooth transition function" mentioned in the article linked to in the bump-function article. The one with the (a, b, c, d) parameters seems like what you're looking for.