The latter method, proposed in the present study, employs the estimator of corrected R a in (11) . Since the data are yearly, the equation (11) needs to be rewritten in discrete-time: (15) where the discrete density function of the generation time, g s is assumed to be given by g s = G(s + 1) − G(s), where G(s) is the cumulative distribution function of the generation time of length s, but g 0 is calculated as a normalized yearly average, because d 1 is as short as 0.24 years.