This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.
 BUILT-IN MATHEMATICA SYMBOL

 LogGammaDistribution represents a log-gamma distribution with shape parameters and and location parameter .
• The probability density for value is proportional to for , and is zero otherwise.
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 log-gamma 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:
Kurtosis depends on the shape parameters:
Different moments with closed forms as functions of parameters:
Hazard function:
Quantile function:
 Applications   (2)
Use LogGammaDistribution to model incomes at a large state university:
Adjust part-time salaries to full-time salaries and select nonzero values:
Fit a Pareto distribution into the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find the average income at the large state university:
Find the probability that a salary is at most \$15000:
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:
Log-gamma distribution can be used to estimate evaluation times:
Fit log-gamma distribution into the data:
Compare the histogram of the data to the PDF of the estimated distribution:
Find the median evaluation time:
Find the upper quartile evaluation time:
Parameter influence on the CDF for each :
Log-gamma distribution is closed under translating by a positive factor:
Relationships to other distributions:
Log-gamma distribution is related to GammaDistribution:
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