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:

Wolfram Research (2010), BenktanderWeibullDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/BenktanderWeibullDistribution.html (updated 2016).

Text

Wolfram Research (2010), BenktanderWeibullDistribution, Wolfram Language function, https://reference.wolfram.com/language/ref/BenktanderWeibullDistribution.html (updated 2016).

BibTeX

@misc{reference.wolfram_2021_benktanderweibulldistribution, author="Wolfram Research", title="{BenktanderWeibullDistribution}", year="2016", howpublished="\url{https://reference.wolfram.com/language/ref/BenktanderWeibullDistribution.html}", note=[Accessed: 24-June-2021 ]}

BibLaTeX

@online{reference.wolfram_2021_benktanderweibulldistribution, organization={Wolfram Research}, title={BenktanderWeibullDistribution}, year={2016}, url={https://reference.wolfram.com/language/ref/BenktanderWeibullDistribution.html}, note=[Accessed: 24-June-2021 ]}

CMS

Wolfram Language. 2010. "BenktanderWeibullDistribution." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2016. https://reference.wolfram.com/language/ref/BenktanderWeibullDistribution.html.

APA

Wolfram Language. (2010). BenktanderWeibullDistribution. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BenktanderWeibullDistribution.html