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 > Heavy Tail Distributions > SinghMaddalaDistribution >
Mathematica > Mathematics and Algorithms > Statistical Data Analysis > Probability & Statistics > Parametric Statistical Distributions > Heavy Tail Distributions > SinghMaddalaDistribution >
BUILT-IN MATHEMATICA SYMBOLSee Also »|More About »

SinghMaddalaDistribution

SinghMaddalaDistribution
represents the Singh-Maddala distribution with shape parameters q and a and scale parameter b.
MORE INFORMATION
  • The probability density for value in a Singh-Maddala distribution is proportional to for .
EXAMPLESCLOSE ALL
Basic Examples   (4)
Probability density function:
Cumulative distribution function:
Mean and variance may not be defined for all parameter values:
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]=
In[4]:=
Click for copyable input
Out[4]=
 
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]=
In[4]:=
Click for copyable input
Out[4]=
 
Mean and variance may not be defined for all parameter values:
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 Singh-Maddala distributed:
Compare its histogram to the PDF:
Distribution parameters estimation:
Estimate the distribution parameters from sample data:
Compare the density histogram of the sample with the PDF of the estimated distribution:
Skewness varies with the shape parameters and and is defined when :
Kurtosis is defined when :
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
Applications   (1)
The number of earthquakes per year can be modeled with SinghMaddalaDistribution:
Fit the distribution to the data:
Compare the data histogram with the PDF of the estimated distribution:
Find the probability of at least 60 earthquakes in the U.S. in a year:
Find the mean amount of earthquakes in the U.S. in a year:
Simulate the number of earthquakes per year for the next 30 years:
Properties & Relations   (9)
Parameter influence on the CDF for each :
Singh-Maddala distribution is closed under scaling by a positive factor:
The family of SinghMaddalaDistribution is closed under a minimum:
The hazard function is unimodal for , and decreasing for :
The parameter q is a scale factor for the hazard function:
Relations to other distributions:
New in 8
Ask a question about this page  |  Suggest an improvement  |  Leave a message for the team
Format:   HTML  |  CDF