The previously shown curves have values of α, β > 1. Setting α = β = 1, the top of the curve is flat. With α, β < 1, the curve inverses, and edge cases become more likely.
With α, β values significantly less than one, edge cases are highly likely, approaching "infinite" likelihood. That is most outcomes would be either the maximum or minimum values, with low probabilities of anything between.
... wait, that is a 'beta fish' !
This plot illustrates the distribution before scaling. Notice that the outcomes are within the range of zero to one.
To obtain a distribution with specific ranges, the minimum desired value must be added to the outcomes and then be multiplied by the range of desired values.