Index of dissimilarity

Calculate the index of dissimilarity between two population structures. A returned value of zero means that the two population have identical structure. A value of 100 means that the populations have no overlap at all (not likely for populations structured only by age). This is a simple measure of distribution overlap on the absolute scale.

ID(pop1, pop2)

Arguments

pop1	numeric. Vector of counts from population 1.
pop2	numeric. Vector of counts from population 2.

Value

The value of the index ranging from 0 to infinity..

Details

Input populations are assumed to be ordered in the same way prior to calling the function. It is only checked that the vectors are of the same length. The input arguments could indeed be populations structured on multiple variables (more than just age), as long as they are ordered in the same way.

References

Siegel Jacob S, Swanson David A (eds.) (2004). The Methods and Materials of Demography, 2 edition. Elsevier Academic Press, California, USA, San Diego, USA.

Examples

pop1                     <- c(7.38,14.16,14.79,17.36,15.11,10.14,8.50,7.28,5.28)
pop2                     <- c(6.48,12.27,15.25,15.10,14.66,10.80,8.95,9.28,7.21)
ID(pop1, pop2)     # 5.5 reproduces table 7.20 of Siegel & Swanson (2004)
#> [1] 5.5
ID(pop1, pop1)     # identical = 0
#> [1] 0
ID(pop1, pop2 * 2) # scale invariant
#> [1] 5.5
pop3                     <- pop4         <- pop1
pop3[1:5]                <- 0
pop4[6:length(pop4)]     <- 0
ID(pop3, pop4)     # no overlap = 100.
#> [1] 100