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I'm doing spatial simulations and I would like to simulate a matrix that represent a truncated 2D-bimodal distribution with U shape. In other words, I would expect high density towards the borders of the matrix and lower density in the middle.

Looking around I have noticed that the distribution that better would fit is the beta distribution. However, do you have any idea of how I could reproduce a 2d beta u shaped density distribution?

I would like to simulate this matrix in R.

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