Fig. 2.

The half-cycle correction (HCC) applied in two discrete-time models approximating a continuous survival function with long (a) and short (b) cycle lengths. The discrete-time approximation error is the lightly shaded area between the continuous survival curve and its discrete approximation represented by the step function. This error is larger in the model with a longer cycle length (a). The standard HCC is shown as the sum of the lightly and darkly shaded areas between the step function and a piecewise linear function joining state membership at the beginning and end of each cycle. a Shows how the HCC from each cycle of length t can be gathered, as represented by the column of shaded triangles, and then summed to yield an area equivalent to half a cycle of state membership at the start of the first cycle, represented by the shaded column