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Characterization of the exponential, Weibull, and Gompertz distributions
| Characteristic | Exponential distribution | Weibull distribution | Gompertz distribution |
|---|---|---|---|
| Parameter | Scale parameter | Scale parameter λ > 0 | Scale parameter λ > 0 |
| λ > 0 | Shape parameter ν > 0 | Shape parameter – ∞ < α < ∞ | |
| Hazard function | h0(t) = λ | h0(t) = λνtν − 1 | h0(t) = λexp(αt) |
| Cumulative hazard function | H0(t) = λt | H0(t) = λtν |  |
| Inverse cumulative hazard | |||
| function |  |
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| Simulating survival | |||
| times (u ∼ U(0,1)) |  |
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