FWE distribution

Freddy Hernandez

2026-02-21

library(RelDists)
#> Loading required package: survival
#> Loading required package: EstimationTools
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#> ><<<<<<<<<<<<<<<<<<<<<<<<   EstimationTools Version 4.3.1   >>>>>>>>>>>>>>>>>>>>>>>><
#>   Feel free to report bugs in https://github.com/Jaimemosg/EstimationTools/issues

Flexible Weibull extension distribution

This distribution was proposed by Bebbington (2007). The probability density function \(f(x)\) and cumulative density function \(F(x)\) are given by:

\[f(x) = \left( \mu+ \frac{\sigma}{x^2} \right) e^{\mu x - \sigma / x} \exp \left( -e^{\mu x - \sigma / x} \right),\]

and

\[F(x) = 1 - \exp[-e^{\mu x - \sigma / x}], \quad x > 0.\]

respectively, where \(\mu > 0\), \(\sigma > 0\) and \(x > 0\).

Next figure shows possible shapes of the \(f(x)\) and \(F(x)\) for several values of the parameters.

Bebbington, M., C. D. Lai, and R. Zitikis. 2007. “A Flexible Weibull Extension.” Reliability Engineering & System Safety 92 (6): 719–26.