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35 lines
1.2 KiB
OCaml
35 lines
1.2 KiB
OCaml
open CCRandom
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let uniformity_test ?(size_hint = 10) k rng st =
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let histogram = Hashtbl.create size_hint in
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let add x =
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let n = try Hashtbl.find histogram x with Not_found -> 0 in
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Hashtbl.replace histogram x (n + 1)
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in
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let () =
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for _i = 0 to k - 1 do
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add (rng st)
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done
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in
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let cardinal = float_of_int (Hashtbl.length histogram) in
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let kf = float_of_int k in
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(* average number of points assuming an uniform distribution *)
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let average = kf /. cardinal in
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(* The number of points is a sum of random variables with binomial distribution *)
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let p = 1. /. cardinal in
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(* The variance of a binomial distribution with average p is *)
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let variance = p *. (1. -. p) in
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(* Central limit theorem: a confidence interval of 4σ provides a false positive rate
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of 0.00634% *)
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let confidence = 4. in
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let std = confidence *. sqrt (kf *. variance) in
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let predicate _key n acc =
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let ( < ) (a : float) b = Stdlib.( < ) a b in
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acc && abs_float (average -. float_of_int n) < std
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in
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Hashtbl.fold predicate histogram true
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let () =
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let st = Random.State.make_self_init () in
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let ok = run ~st (uniformity_test 50_000 (split_list 10 ~len:3)) in
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if not ok then failwith "uniformity check failed"
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