Possible models for quasi-composite distributions

In order to find possible models for the quasi-composite distribution (the distribution which takes the form of a smooth-angled line on probability paper as shown in Fig. 1), the graphical behavior on probability paper of the mixed distribution model, the convoluted distribution model and the competing-risk distribution model are examined. It is shown that the convoluted as well as the mixed distribution can be models for the distribution of the form of Fig. 1(a), and that the competing-risk and the mixed distribution can be models for the distribution of the form of Fig. 1(b). It is also shown that the mixed distribution generally takes the form of an S-shaped curve.