ArcSinDistribution

Generate a set of pseudorandom numbers that are arc sine distributed:

Compare the histogram to the PDF:

Distribution parameters estimation:

Estimate the distribution parameters from sample data:

Compare the density histogram of the sample with the PDF of the estimated distribution:

Skewness and kurtosis are constant:

Different moments with closed forms as functions of parameters:

Moment:

CentralMoment:

Closed form for symbolic order:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

The arc sine distribution is the limiting distribution of the proportion of time spent on the positive side by a simple symmetric random walk. Simulate a symmetric random walk:

Calculate the ratio of time spent on the positive side:

In the limit the ratio has arc sine distribution:

Parameter influence on the CDF for each :

Arc sine distribution is closed under translation and scaling by a positive factor:

The CDF depends on the ArcSin function:

The square of an arc sine distribution over has arc sine distribution over :

Relationships to other distributions:

BetaDistribution is a special case of arc sine distribution:

Arc sine distribution is a special type of type 1 PearsonDistribution:

HoytDistribution can be obtained from ExponentialDistribution and ArcSinDistribution: