We covered the classic exponential distribution in Section 12.7. Here we describe a range of extensions.
The generalised exponential distribution, confusingly, can be referred to by using the same GED acronym as the generalised error distribution that we covered in Section 20.12. Less ambiguously known as the exponentiated exponential distribution, it extends the exponential distribution by adding a shape parameter (δ). It is described by
Fitting to the intervals between events of the LPG splitter reflux exceeding 65 m3/hr gives α as 0.0626, β as 12.5 and δ as 0.950. With δ so close to 1, in this case RSS is only slightly improved, from 0.0058 for the classic exponential distribution, to 0.0053.
The Gompertz–Verhulst distribution includes another shape parameter. It is described by
If δ1 is set to 1, the distribution reverts to the generalised exponential distribution. ...