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 > Exponential-Related Distributions > ExpGammaDistribution >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Exponential-Related Distributions > ExpGammaDistribution >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

ExpGammaDistribution

ExpGammaDistribution
represents an exp-gamma distribution with shape parameter , scale parameter , and location parameter .
MORE INFORMATION
  • The survival function for value in an exp-gamma distribution is proportional to .
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]=
 
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]=
Scope   (7)
Generate a set of pseudorandom numbers that are exp-gamma 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:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
Applications   (1)
ExpGammaDistribution can be used to model monthly maximum wind speeds:
Fit the distribution into the data:
Compare the histogram of the data with the PDF of the estimated distribution:
Find the probability of monthly maximum wind exceeding 70 km/h:
Find the average monthly maximum wind speed:
Simulate maximum wind speed for 30 months:
Properties & Relations   (7)
Parameter influence on the CDF for each :
Exp-gamma distribution is closed under translation and scaling by a positive factor:
Relationships to other distributions:
ExpGammaDistribution is a transformation of GammaDistribution:
Exp-gamma distribution is a special case of MinStableDistribution:
New in 8
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF