Beta distribution

I want to have a distribution similar to U-shape beta distribution as the following:

I want to make the distribution as :

Any idea?

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Ambassador to the humans
All of the values are between 0 and 1. I'm just not understanding you. Can you make a sketch of what you're talking about? Or try phrasing it differently?
Oh, I get the request now.

@menahg can you explain the context you are working in or what this will be used for?
@hlsmith I intend to use it for a simulation, to model a decision for sharing an opinion among agents. It is a Beta distribution, but I want to increase the probability in the middle a little.
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Less is more. Stay pure. Stay poor.
Probably not an option, but in Bayesian modeling I keep seeing the "horse shoe" prior which has a similar shape.