axMidpoint approximates a(x) using interval midpoints
approximates a(x) using interval midpoints (except a0, which is estimated using a rule-of-thumb formula scaled by m0)
a numeric vector of central death rates, defined as deaths/exposure.
a numeric vector of the age-interval widths. Must be the same length as Mx.
All values will be in the exact middle of the age interval, except for a0, which uses:
a0 = .07 + 1.7 * M0.
returns a numeric vector of ax values
formula for a0 as suggested by: Keyfitz, N. (1970), Finding probabilities from observed rates, or how to make a life table. The American Statistician (1970), pp. 28-33
axEstimate, a wrapper function for this and 3 other a(x) estimation methods (
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