Continuous and differentiable bell-shaped distribution on $[a, b]$ Is there a distribution with these three properties?

*

*Supported on $[a, b]$ for any $a, b\in\mathbb{R}$ and $a < b$

*Continuous and Differentiable (that is $\nabla_x p(x)$ can be computed)

*Bell-curved (or at least not as flat as the Uniform(a, b))


The Truncated normal distribution obeys all prerequisites:

*

*It's bell shaped

*It's continuous

*Its support is $x \in [a,b]$

*It's differentiable, i.e. $\nabla_x p(x)$ exists for all $x \in [a,b]$
