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

# BenktanderWeibullDistribution

 BenktanderWeibullDistribution represents a Benktander distribution of type II with parameters a and b.
• The probability density for a value in a Benktander-Weibull 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 have Benktander-Weibull 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:
Kurtosis:
Different moments with closed forms as functions of parameters:
Closed form for symbolic order:
Hazard function:
Quantile function:
 Applications   (2)
Compute the mean excess function for a Benktander type II distribution:
For large it approaches that of a Weibull distribution:
Now replace the incomplete function with its asymptotics at large arguments:
Find a stationary renewal distribution associated with a Benktander type I distribution:
Survival function:
Compare with a truncated WeibullDistribution:
Parameter influence on the CDF for each :
BenktanderWeibullDistribution is subexponential for :
Relationships to other distributions:
When Benktander type II reduces to a truncated ExponentialDistribution:
Shifted ExponentialDistribution is a Benktander type II distribution:
A ParetoDistribution is the limiting case of the Benktander type II distribution:
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