romaniuk: Romaniuk Fertility Model Schedule.
In gjabel/agesched: Demographic Age Schedules

Description Usage Arguments Value Author(s) References See Also Examples

Provides a scaled Romaniuk fertility schedule,

f(x) = f(x) = ≤ft( 1 + \frac{x}{m-α} \right) ^≤ft\{ \frac{(M-α) [β-2(A-α)]}{β(A-M)} \right\}≤ft( 1 - \frac{x}{δ - M + α} \right)^≤ft\{ \frac{(δ - M+α)[δ-2(A-α)]}{δ(A-M)} \right\}

for a given set of parameter values and sequence of ages.

1 2	romaniuk(tfr = NULL, x = seq(from = 0, to = 100, by = 1), mean_cb = NULL, mode_cb = NULL, start_fertage = 15, width_fertage = 35, scaled = TRUE)

`tfr`	Total fertility rate of the returned age schedule. Equivalent to \T in the equation above.
`x`	Vector for the sequence of ages.
`mean_cb`	Numeric value for the mean age of mothers at child birth. Equivalent to a in the equation above.
`mode_cb`	Numeric value for the modal age of mothers at child birth. Equivalent to m in the equation above.
`start_fertage`	Numeric value for the start of the fertility age range. Equivalent to α in the equation above.
`width_fertage`	Numeric value for the width of the fertility age range. Equivalent to δ in the equation above.
`scaled`	Boolean value to return age specific fertility rates that scale to sum to `tfr` or not. Default `TRUE`.

Returns the f(x) values from the Romaniuk schedule of age specific fertility. The age range for the calculation can take any sequence of positive numbers, such as ages in single or 5-year intervals. The function is primarily intended for use in decomposing a total fertility rate into an age-specific values.

The parameters relate to the mean and modal central measures (mean_cb, mode_cb) and the ages of mothers at child birth (start_cb, width_cb).

Also known as Mitra's Pearsonian Type I function or Beta funtion. The adapted version in this function, to allow scaling to a known TFR, was based on IUSSP Demographic Models online section (see http://papp.iussp.org/sessions/papp103_s03/PAPP103_s03_040_070.html for more details).

Guy J. Abel

Romaniuk, A. (1973). "A three parameter mode for birth projections", Population Studies 27(3):467-478. doi 10.2307/2173766

Mitra, S. and Romaniuk, A. (1973). 'Pearsonian Type I Curve and its Fertility Projection Potentials'. Demography 10(3): 351-365. doi 10.2307/2060844

.

#single year
f0 <- romaniuk(tfr = 3, mean_cb = 27, mode_cb = 26)
plot(f0, type = "l")

#five year
f1 <- romaniuk(tfr = 5.8, x = seq(0, 100, 5), mean_cb = 28, mode_cb = 23)
plot(f1, type = "l")
sum(f1) * 5