Arcsine distribution


In probability theory, the arcsine distribution is the probability distribution whose cumulative distribution function is
for 0 ≤ x ≤ 1, and whose probability density function is
on . The standard arcsine distribution is a special case of the beta distribution with α = β = 1/2. That is, if is the standard arcsine distribution then.
The arcsine distribution appears

Arbitrary bounded support

The distribution can be expanded to include any bounded support from a ≤ x ≤ b by a simple transformation
for a ≤ x ≤ b, and whose probability density function is
on .

Shape factor

The generalized standard arcsine distribution on with probability density function
is also a special case of the beta distribution with parameters.
Note that when the general arcsine distribution reduces to the standard distribution listed above.

Properties