I would like to have a formula to generate the curves shown in the following plot:
The magnitude of curvature should be adjusted by a parameter. Does there exist any well-known function or distribution to define such curves?
2026-05-15 08:31:05.1778833865
How to find the formulas for a "perfect-bell" curve between 0-1?
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How about $(1-(1-x)^p)^{1/p}$? These are symmetric across the line $y = 1 - x$.
For $p=1, 2, 3, 4, 5$ (moving up and to the left as $p$ increases):