Reband any discrete distribution

e.g. age banded population, or a discrete probability distribution e.g. a serial interval distribution. This method fits a monotonically increasing spline to the cumulative distribution (including the upper and lower limits) and interpolating using that spline to the new cut points.

Usage

reband_discrete(
  x,
  y,
  xout,
  xlim = c(0, NA),
  ytotal = c(0, sum(y)),
  digits = 0,
  labelling = c("positive_integer", "inclusive", "exclusive"),
  sep = "-"
)

Arguments

x

a set of upper limits of bands, e.g. for age: 0-14;15-64;65-79;80+ is 15,65,80,NA

y

a set of quantities for each band e.g. population figures

xout

a set of new upper limits

xlim

Upper and lower limits for x. if the last band is e.g 80+ in the input and we want to know the 85+ band in the output some kind of maximum upper limit is needed to interpolate to.

ytotal

upper and lower limits for y. If the interpolation values fall outside of x then the minimum and maximum limits of y are given by this. This would be c(0,1) for a probability distribution, for example.

digits

if the xout value is continuous then how many significant figures to put in the labels

labelling

are the xout values interpretable as an inclusive upper limit, or an exclusive upper limit, or as an upper limit of an `positive_integer“ quantity

sep

separator for names e.g. 18-24 or 18 to 24

Value

a re-banded set of discrete values, guaranteed to sum to the same as y

Examples

england_demographics = ukc19::uk_population_2019_by_10yr_age %>%
  dplyr::filter(name=="England")

ul = stringr::str_extract(england_demographics$class, "_([0-9]+)",group = 1) %>%
  as.numeric()
# ul is currently inclusive so add 1:
ul = ul + 1

tmp = reband_discrete(
  ul, england_demographics$population,
  c(5,10,15,40,80), xlim=c(0,120))

tmp
#>      0-4      5-9    10-14    15-39    40-79      80+ 
#>  3443507  3394336  3194025 18081321 25336808  2836964 

sum(tmp)
#> [1] 56286961
sum(england_demographics$population)
#> [1] 56286961