Expected hits proportional to size

Turns a size measure into the expected hits Chromy's selection consumes. In the usual case (min_replacement = FALSE) units whose proportional share reaches one are made certainties and the remainder is re-shared until no unit crosses one; the result is a vector of inclusion probabilities in [0, 1], and n may not exceed the number of units with positive size. Under minimum replacement the expected hits are simply n times the size shares, values above one meaning the unit may be selected more than once — which Chromy's procedure handles natively, and is the reason to use it.

Usage

expected_hits(size, n, min_replacement = FALSE)

Arguments

size

Non-negative numeric vector, one entry per unit.

n

The sample size: the expected number of selections.

min_replacement

Allow expected hits above one instead of resolving certainties.

Value

A numeric vector of expected hits summing to n.

Examples

expected_hits(c(100, 50, 10, 5, 5), 3)
#> [1] 1.00 1.00 0.50 0.25 0.25
expected_hits(c(100, 50, 10, 5, 5), 3, min_replacement = TRUE)
#> [1] 1.76470588 0.88235294 0.17647059 0.08823529 0.08823529