# FWE distribution

#### 2022-12-21

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# 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.