Survival distributions based on the XD model class

We aim to explore the survival distributions based on the extreme dispersion, XD, models proposed by Jørgensen (2010). It is suggested that survival times can be modelled within the XD framework by taking log T = Y ~ XD( µ,𝜆 ), where T is the survival time and Y is the extreme dispersion random variable. We will show how these survival models can be generated using XD and look at the distribution and properties of the survival time T = eY .