Probability density function
Cumulative distribution function
for 0 ≤ x ≤ 1, and whose probability density function is
on (0, 1). 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 (a, b).
The generalized standard arcsine distribution on (0,1) 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.
- Arcsine distribution is closed under translation and scaling by a positive factor
- The square of an arc sine distribution over (-1, 1) has arc sine distribution over (0, 1)