This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

PowerDistribution

PowerDistribution
represents a power distribution with domain parameter k and shape parameter a.
  • The probability density for value in a power distribution is proportional to for and zero otherwise.
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]=
In[3]:=
Click for copyable input
Out[3]=
 
Cumulative distribution function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
In[3]:=
Click for copyable input
Out[3]=
 
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 power distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare a density histogram of the sample with the PDF of the estimated distribution:
Skewness depends only on the shape parameter:
Limiting values:
Kurtosis depends only on the shape parameter:
Limiting values:
Kurtosis attains its minimum:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Closed form for symbolic order:
Hazard function:
Quantile function:
Suppose the variance of a normal variate follows PowerDistribution defined on the unit interval. Find the resulting distribution:
Generate random variates:
Compare a sample histogram to the distribution density:
Parameter influence on the CDF for each :
Power distribution is closed under scaling by a positive factor:
Relationships to other distributions:
KumaraswamyDistribution simplifies to a special case of power distribution:
Power distribution is a transformation of ExponentialDistribution:
Power distribution is a distribution of an inverse of ParetoDistribution:
New in 8