FWE distribution

Freddy Hernandez

2024-07-09

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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.