Asked at SO but it seems no one have an idea, so I'm coming again.
Suppose I have 3 data points ($(0, 0), (0 < t_2 < 1, 0 < y_2 < 1), (1, 1))$ and I want to use a monotonic function to interpolate the points. I know that directly fitting a Beta CDF would be a theoretical way (though I'm still finding a way to do so) but is there any alternatives? Thanks in advance.