Smoothing of an age structure by single years using Spencer's formula.

Source: R/SPENCER.R

Spencer's method is used to adjust distributions by year of age based on cumulative series.

spencer(Value, Age)

Arguments

Value

numeric. A vector of demographic counts in single age groups.
Age

numeric or character. A vector with ages in single years.

Value

A named vector with the smoothed age structure.

Details

Single year age groups are assumed.

References

Roger G, Waltisperger D, Corbille-Guitton C (1981). Les structures par sexe et âge en Afrique. GDA, Paris, France. Roger et al (1981, pp. 373-377).

Examples

# data from GDA1981IREDA, Table 15 and 16, page 375-376: Ghana (1970 Males + Females),
# population between 10 and 40 years by single age.
Pop  <-c(286487,282182,319718,345610,329133,324683,330555,269536,271593,253798,
         242297,165755,233159,185812,175647,187138,160864,128099,178568,123386,
         194999,113372,139088,106190,127482,178375,123286,95637,151514,82614,
         239243,74788,112354,61746,72366,144828,92563,53924,94635,52351,178832)
Age  <-c(0:40)
sp_smoothed <- spencer(Value    =Pop,Age=Age)
 if (FALSE) {
plot(Age,Pop, col               = "red", xlab = "Age", ylab = "Population",type ='l')
lines(Age,spencer(Pop,Age), col = "blue")
legend("topright",
lty                             =1,
col                             = c("red","blue"),
legend                          =  c("Original","Spencer"))
}
# on the fly unit test:
Tab16answer <- c(rep(NA,10),233847,216876,201938,189873,179734,171529,164280,158214,
 152477,147735,143099,139301,135930,133889,132458,132495,
 132660,132894,131463,128560,123150,116725,109180,102386,
 96394,92586,89962,88681,86812,84209,79819)
stopifnot(all(na.omit(abs(sp_smoothed - Tab16answer) < 0.5)))