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 > Discrete Statistical Distributions >
Mathematica > Mathematics and Algorithms > Statistics > Statistical Distributions > Discrete Statistical Distributions >
Built-in Mathematica SymbolTutorials »|See Also »|More About »

ZipfDistribution

ZipfDistribution[Rho]
represents a Zipf distribution with parameter Rho.
  • The probability for value x in a Zipf distribution is proportional to x^(-rho-1) if x is a positive integer, and is zero otherwise. »
EXAMPLESCLOSE ALL
Basic Examples   (2)
Mean and variance of a Zipf distribution:
Probability density function:
Mean and variance of a Zipf 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 have a Zipf distribution:
Properties based on higher-order moments:
Second moment of a Zipf distribution:
Applications   (2)
Plot the cumulative distribution function of a Zipf distribution:
The density functions of Zipf variables are highest for small positive integers:
Properties & Relations   (3)
The probability of getting any real number except a positive integer is zero:
The probability mass and random variable have a power law relationship:
Moments can be obtained from the characteristic function:
Possible Issues   (2)
ZipfDistribution is not defined when Rho is non-positive:
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