Translation Formulae for Non-repeatable Events

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Abstract
Ryder's translation expressions for repeatable events are extended to the case of non-repeatable events. It is found that cohort quantum is a constant function of time when period quantum is constant, and period tempo, as measured by the moments of the age pattern of the occurrence-exposure rates, change linearly with time. The degree of distributional distortion (that is, the upward or downward shift in cohort caused by changes in the period age pattern), given a set of occurrence-exposure rates, is generally less for non-repeatable than for repeatable events in this case, in particular at high quantum levels. Furthermore, it is found that when period tempo is constant over time, and period quantum falls linearly, period quantum underestimates cohort quantum for high period quantum levels, and overestimates it for low period quantum levels.

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