Following Distribution that has a range from 0 to 1 and with peak between them?, I generated a beta distribution that has a peak between 0 and 1 at the mean value. When the mean value is 0.5, I can change the variance and get different shapes as shown below: [![enter image description here][1]][1]

However, when the mean value is too close to 0 or 1 (either extreme), I couldn't manage to get a wide (similar to the uniform dist) distribution as you can see below: [![enter image description here][2]][2]

Does anyone know how to solve this problem? i.e. be able to create different shapes of distribution for every mean value in the range 0-1. [1]: https://i.sstatic.net/HKPoH.png [2]: https://i.sstatic.net/DsN6u.png

Following Distribution that has a range from 0 to 1 and with peak between them?, I generated a beta distribution that has a peak between 0 and 1 at the mean value. When the mean value is 0.5, I can change the variance and get different shapes as shown below:

However, when the mean value is too close to 0 or 1 (either extreme), I couldn't manage to get a wide (similar to the uniform dist) distribution as you can see below:

Does anyone know how to solve this problem? i.e. be able to create different shapes of distribution for every mean value in the range 0-1.