This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

 SinghMaddalaDistribution represents the Singh-Maddala distribution with shape parameters q and a and scale parameter b.
• The probability density for value in a Singh-Maddala distribution is proportional to for .
Probability density function:
Cumulative distribution function:
Mean and variance may not be defined for all parameter values:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance may not be defined for all parameter values:
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Median:
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 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:
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