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

 DavisDistributionrepresents a Davis distribution with scale parameter b, shape parameter n, and location parameter .
• The probability density for value in a Davis distribution is proportional to for .
• DavisDistribution allows b to be any positive real number, to be any non-negative real number, and .
Probability density function:
Cumulative distribution function:
Mean and variance:
Probability density function:
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Cumulative distribution function:
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Mean and variance:
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 Scope   (7)
Generate a set of pseudorandom numbers that have Davis distribution:
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 only on shape parameter n:
Kurtosis depends only on shape parameter n:
Different moments with closed forms as functions of parameters:
Hazard function:
Quantile function:
 Applications   (2)
DavisDistribution can be used to model incomes:
Adjust part-time to full-time and select nonzero values:
Fit Davis distribution into the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find average income at a large state university:
Find the probability that a salary is at most \$150,000:
Find the probability that a salary is at least \$150,000:
Find the median salary:
Simulate the incomes for 100 randomly selected employees of such a university:
BetaPrimeDistribution can be used to model state per capita incomes:
Fit Davis distribution into the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find 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 log-likelihood value:
Compare with the fit using BetaPrimeDistribution:
Compare with the fit using DagumDistribution:
Compare with the fit using LogLogisticDistribution:
Parameter influence on the CDF for each :
Davis distribution is closed under translation and scaling by a positive factor:
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