Arcsine Distribution

The Arcsine distribution is a special form of the Beta distribution where both shape parameters are equal to 0.5.

There is one standard arcsine distribution. The Cumulative Distribution Function (CDF) is:

$$F(x) = \frac{2}{\pi}\arctan \sqrt{x}$$

for \(x \in [0, 1]\).

The arcsine distribution is implemented by the ArcsineDistribution class. The implementation allows for distributions over a non-standard interval. It has two constructors. The first constructor takes no arguments and returns the standard arcsine distribution over [0, 1]. The second constructor thakes two arguments: the lower and upper bounds of the distribution.

var arcsine1 = new ArcsineDistribution(-1, 1);

A singleton instance of the standard distribution is available as the Standard property. The code below draws a random sample from the standard distribution:

var random = new MersenneTwister();
double sample = ArcsineDistribution.Standard.Sample(random);

For details of the properties and methods common to all continuous distribution classes, see the topic on continuous distributions..