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

 DagumDistribution represents a Dagum distribution with shape parameters p and a and scale parameter b.
• The probability density for value in a Dagum distribution is proportional to for .
Probability density function:
Cumulative distribution function:
Mean and variance:
Median:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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Median:
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 Scope   (7)
Generate a set of pseudorandom numbers that are Dagum 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 depends on the shape parameters a and p and is defined for :
Kurtosis is defined for :
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function is unimodal for and decreasing otherwise:
Quantile function:
 Applications   (4)
DagumDistribution can be used to model incomes:
Adjust part-time to full-time and select nonzero values:
Fit Dagum distribution into the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find the average income at a large state university:
Find the probability that a salary is at most \$150000:
Find the probability that a salary is at least \$150000:
Find the median salary:
Simulate the incomes for 100 randomly selected employees of such a university:
DagumDistribution can be used to model state per-capita incomes:
Fit a Dagum distribution into the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find the average income per capita:
Find states with income close to the average:
Find the median income per capita:
Find states with income close to the median:
Find the log-likelihood value:
Compare with the fit using BetaPrimeDistribution:
Compare with the fit using DavisDistribution:
Compare with the fit using LogLogisticDistribution:
DagumDistribution can be used to model size; consider the depth (in mm) of leptograpsus crabs:
Fit a Dagum distribution into the data:
Compare the histogram of the data with the PDF of the estimated distribution:
Find the average depth of a crab:
Find the probability that a crab is deeper than 15 mm:
Simulate depths of 30 crabs:
DagumDistribution can be used to model waiting times:
Fit a Dagum distribution to the data:
Compare the histogram of the data with the PDF of the estimated distribution:
The fit is almost as good as the one with ExponentialDistribution:
Find the average number of days between major earthquakes:
Find the probability that there are at least 200 days between two serious earthquakes:
Parameter influence on the CDF for each :
Dagum distribution is closed under scaling by a positive factor:
The Dagum distribution is unimodal for , and zero modal otherwise:
Relationships to other distributions:
New in 8