Gompertz (Truncated Gumbel) DistributionΒΆ

For \(x\geq0\) and \(c>0\) . In JKB the two shape parameters \(b,a\) are reduced to the single shape-parameter \(c=b/a\) . As \(a\) is just a scale parameter when \(a\neq0\) . If \(a=0,\) the distribution reduces to the exponential distribution scaled by \(1/b.\) Thus, the standard form is given as

\begin{eqnarray*} f\left(x;c\right) & = & ce^{x}\exp\left(-c\left(e^{x}-1\right)\right)\\ F\left(x;c\right) & = & 1-\exp\left(-c\left(e^{x}-1\right)\right)\\ G\left(q;c\right) & = & \log\left(1-\frac{1}{c}\log\left(1-q\right)\right)\end{eqnarray*}



Implementation: scipy.stats.gompertz

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Gumbel (LogWeibull, Fisher-Tippetts, Type I Extreme Value) Distribution