This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.1)

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:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Cumulative distribution function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Mean and variance:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Median:
In[1]:=
Click for copyable input
Out[1]=
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:
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