3. (HSD model). The health(H)-sickness(S)-death(D) model has 3 states {H, S, D} and transition rates The observations for a subject • the times between successive transitions; the numbers of transitions

of each type. • V; = waiting time of the ith subject in the healthy state; W; = waiting time of the ith subject in the sick state; Si = number of transition H → S by the ith subject; R: = number of transition S → H by the ith subiect: Dinumber of transition H → D by the ith subject;B Ui = number of transition SD by the ith subject let v, w, s, r, d, u be observed values of V, W, S, R, D, U, respectively. \text { - let } V=\sum_{i=1}^{N} V_{i}, W=\sum_{i=1}^{N} W_{i}, S=\sum_{i=1} S_{i}, R=\sum_{i=1}^{N} R_{i}, D=\sum_{i=1}^{N} D_{i}, U=\sum_{i=1}^{N} U_{i}