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Sampling from items with known proportions.
open System
// Sample with replacement
let replaceSampler (rng: Random) (counts: int[]) =
let N = counts |> Array.sum
let draw = rng.Next(N)
let rec find index cumul =
let n = counts.[index]
if draw < (cumul + n)
then index
else find (index + 1) (cumul + n)
find 0 0
// Sample without replacement
let sampler (rng:Random) (counts:int[]) =
let counts = Array.copy counts
let N = counts |> Array.sum
let draw = rng.Next(N)
let rec find index cumul =
let n = counts.[index]
if draw < (cumul + n)
then
let updatedCounts = counts
updatedCounts.[index] <- counts.[index] - 1
(index, updatedCounts)
else find (index + 1) (cumul + n)
find 0 0
// Usage / example
let rng = Random()
let replace = replaceSampler rng
let counts = [| 10; 40; 50 |]
// Sequence should contain
// roughly 10%, 40%, 50% of 0, 1, 2
[ for i in 1 .. 100000 -> replace counts ]
|> Seq.countBy id
|> Seq.toList
let noReplace = sampler rng
let sample =
Seq.unfold (fun (counts:int[]) ->
let (i, updatedCounts) = noReplace counts
Some(i, updatedCounts))
sample counts |> Seq.take 50 |> Seq.countBy id |> Seq.toList
sample counts |> Seq.take 100 |> Seq.countBy id |> Seq.toList
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