BenktanderWeibullDistribution

BenktanderWeibullDistribution[a,b]

represents a Benktander distribution of type II with parameters a and b.

Details

Background & Context

Examples

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Basic Examples  (4)

Probability density function:

Cumulative distribution function:

Mean and variance:

Median:

Scope  (8)

Generate a sample of pseudorandom numbers from a BenktanderWeibull 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:

Moment:

Closed form for symbolic order:

CentralMoment:

FactorialMoment:

Cumulant:

Hazard function:

Quantile function:

Use dimensionless Quantity to define BenktanderWeibullDistribution:

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 II distribution:

Survival function:

Compare with a truncated WeibullDistribution:

Properties & Relations  (5)

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:

Neat Examples  (1)

PDFs for different a values with CDF contours:

Introduced in 2010
 (8.0)
 |
Updated in 2016
 (10.4)