I’m looking for a density function $\rho(x)$ that is zero from $-\infty$ to, say, $a$, and then “bell-shaped” from $a$ to $\infty$. (In other words, it starts at zero at $a$, then rises until it reaches a peak, and then decreases again, and approaches zero as $x\to\infty$.)
Is there any famous and well-known density function like that, or do I have to construct my own using some piecewise trickery? (The latter is easy to do. However, it would be best if I could find a ready-made density function in the stockpile of well-known density functions.)