As one of the more commonly used distributions, the classic beta distribution was described in Section 12.3. Here we cover special cases and enhancements.
Setting, in Equation (12.13), both δ1 and δ2 to 0.5 gives the special case known as the arcsine distribution
It is the CDF that gives the distribution its name
Inverting give the QF
Statistical parameters are
There is also the second kind of the arc‐sine distribution; its PDF is
Figure 25.1 shows both kinds. Without a shape factor they cannot be fitted to data but, in any case, it is difficult to see what application either of the anti‐modal distributions ...