Mathematica 9 is now available
SEARCH MATHEMATICA 8 DOCUMENTATION
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Mathematica > Data Manipulation > Statistics > Statistical Distributions > Continuous Statistical Distributions >
Mathematica > Mathematics and Algorithms > Statistics > Statistical Distributions > Continuous Statistical Distributions >
Built-in Mathematica SymbolTutorials »|More About »

ParetoDistribution

ParetoDistribution[k, Alpha]
represents a Pareto distribution with minimum value parameter k and shape parameter Alpha.
  • The probability density for value x in a Pareto distribution is proportional to x^(-alpha-1) for x>k, and is zero for x<k. »
EXAMPLESCLOSE ALL
Basic Examples   (2)
The mean and variance of a Pareto distribution:
Probability density function:
The mean and variance of a Pareto distribution:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
 
Probability density function:
In[1]:=
Click for copyable input
Out[1]=
In[2]:=
Click for copyable input
Out[2]=
Scope   (3)
Generate a set of pseudorandom numbers that are Pareto distributed:
Properties based on higher-order moments:
The q^(th) quantile of a Pareto distribution:
Applications   (2)
Plot the cumulative distribution function of the random variable:
A contour plot as both x and Alpha are varied:
Properties & Relations   (2)
The probability density function integrates to unity:
The probability density and random variable have a power-law relationship:
Possible Issues   (2)
ParetoDistribution is not defined when k is not a real number:
ParetoDistribution is not defined when Alpha is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
New in 6
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team