Arcsine distribution

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Template:Probability 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 (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

Generalization

Template:Probability distribution

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 (ab).

Shape factor

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.

Properties

Differential equation

Related distributions

See also

References

  1. REDIRECT Template:Probability distributions

Template:Common univariate probability distributions