Mathematica 9 is now available
THIS IS DOCUMENTATION FOR AN OBSOLETE PRODUCT.
SEE THE DOCUMENTATION CENTER FOR THE LATEST INFORMATION.
Wolfram Mathematica Documentation Center
DOCUMENTATION CENTER SEARCH
New to Mathematica? Find your learning path »
Mathematica > Data Manipulation > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Bounded Domain Distributions > KumaraswamyDistribution >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Bounded Domain Distributions > KumaraswamyDistribution >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

KumaraswamyDistribution

KumaraswamyDistribution
represents a Kumaraswamy distribution with shape parameters and .
MORE INFORMATION
  • The probability density for value is proportional to for , and is zero elsewhere.
EXAMPLESCLOSE ALL
Basic Examples   (4)
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]=
Scope   (7)
Generate a set of pseudorandom numbers that are Kumaraswamy 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:
Kurtosis:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function has a bathtub shape for :
Quantile function:
Applications   (1)
KumaraswamyDistribution can be used in hydrology; consider monthly water levels at Lake Mead:
According to the Arizona Game and Fish Department, the maximum lake level is 1229 feet:
Fit Kumaraswamy distribution into the data:
Compare the histogram of the data with the estimated distribution:
Find the probability that Lake Mead is below drought level (1125 feet):
Find the average water level in feet:
Simulate the water levels for the next three years (with respect to the drought level):
Properties & Relations   (5)
Parameter influence on the CDF for each :
Relationships to other distributions:
Kumaraswamy distribution is a transformation of a BetaDistribution:
Kumaraswamy distribution simplifies to a BetaDistribution:
Kumaraswamy distribution simplifies to a PowerDistribution:
New in 8
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF