gamma_fert: Gamma Fertility Model Schedule.
In gjabel/agesched: Demographic Age Schedules

Description Usage Arguments Value Author(s) See Also Examples

Provides a scaled gamma fertility schedule,

f(x) = \frac{1}{Γ(k)θ^k} x^{(k-1)}e^{-\frac{x}{θ}}

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

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gamma_fert(tfr = NULL, x = seq(from = 0, to = 100, by = 1),
  mean_cb = NULL, shape = NULL, start_fertage = 15, width_fertage = 35,
  ...)

`tfr`	Numeric value for total fertitliy rate of the returned age schedule.
`x`	Vector for the sequence of ages.
`mean_cb`	Numeric value for the mean age of mothers at child birth. Equivalent to kθ.
`shape`	Numeric poisitive value for schedule shape. Used direcly in `dgamma`.
`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.
`...`	Additional arguments passed to `dgamma`

Returns the f(x) values from a gamma 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 the mean age of child bearing (mean_cb) and the shape of the schedule (shape). The shape and mean age parameters are used to determine the scale parameter of the gamma distribution.

The arguments for the start and width of the fertility age range (start_fertage, width_fertage) are used to select where the gamma distribution is applied over the range of ages given in x.

Guy J. Abel

gage romainuk hadwiger

#single year
f0 <- gamma_fert(tfr = 4, mean_cb = 25, shape = 5)
plot(f0, type = "l")

#five year
f1 <- gamma_fert(tfr = 5.8, mean_cb = 28, x = seq(from = 0, to = 100, by = 5), shape = 3)
plot(f1, type = "l")
sum(f1) * 5