This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

# ArcSinDistribution

 ArcSinDistribution represents the arc sine distribution supported between and .
• The probability density for value in an arc sine distribution is proportional to for , and is zero for or .
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
 Out[1]=
 Out[2]=

Cumulative distribution function:
 Out[1]=
 Out[2]=

Mean and variance:
 Out[1]=
 Out[2]=

Median:
 Out[1]=
 Scope   (6)
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:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (1)
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:
New in 8