Statistics for Process Control Engineers

28Exponential Distribution

We covered the classic exponential distribution in Section 12.7. Here we describe a range of extensions.

28.1 Generalised Exponential

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

(28.1)

(28.2)

(28.3)

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.

28.2 Gompertz–Verhulst

The Gompertz–Verhulst distribution^[22] includes another shape parameter. It is described by

(28.4)

(28.5)

If δ₁ is set to 1, the distribution reverts to the generalised exponential distribution. ...