which is the distribution of those who died before time to, but would have been age z at to if they had lived. If I(z) = I, the distribution is f (t\a(z\to) =0)= Zt\q(fL+ for t < z.

Note that if z ^<x>, then f (t\a(z\to)=0) = q(t) which is the population survival pdf.

3.4 Chronological Time Modeling

Suppose that the incidence is a function of chronological time rather than age-Also, in some cases, to may be regarded as far removed from the origin as the disease process has been going on a long time. Then the equations for the forward and backward times may be modified by replacing z by to- Therefore, we have

/■to qf (t\to)= i I(t)q(to - t + t)dt/P(to) o qb(t\to) = I(to - t)Q(t)/P(to)

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