Benford's law: Difference between revisions
Content added Content deleted
| Line 1,979: | Line 1,979: | ||
χ² = 3204.8072</pre> |
χ² = 3204.8072</pre> |
||
=={{header|Julia}}== |
=={{header|Julia}}== |
||
<syntaxhighlight lang="julia">using BenchmarkTools, Printf |
|||
# fast Fibonacci number iterator |
|||
<syntaxhighlight lang="julia">fib(n) = ([one(n) one(n) ; one(n) zero(n)]^n)[1,2] |
|||
struct Fib end |
|||
Base.iterate(::Fib, (a, b) = (big(1), big(1))) = a, (b, a + b) |
|||
Base.eltype(::Type{Fib}) = BigInt |
|||
Base.IteratorSize(::Type{Fib}) = Base.IsInfinite() |
|||
fib(n) = Iterators.take(Fib(), n) |
|||
# relative frequency of first digits in a list of numbers |
|||
ben(l) = [count(x->x==i, map(n->string(n)[1],l)) for i='1':'9']./length(l) |
|||
function benford_freq(list) |
|||
counts = zeros(Int, 9) |
|||
foreach(n -> counts[parse(Int, first(string(n)))] += 1, list) |
|||
counts ./ sum(counts) |
|||
end |
|||
@btime benford_freq(fib(1000)) |
|||
benford(l) = [Number[1:9;] ben(l) log10(1.+1./[1:9;])]</syntaxhighlight> |
|||
# Benfords law |
|||
P(d) = log10(1 + 1 / d) |
|||
# compare a list of numbers to Benfords law (pretty printing) |
|||
function benford(list) |
|||
println("\nd Freq(d) P(d)") |
|||
for (d, a) ∈ enumerate(benford_freq(list)) |
|||
comp(a, b) = isapprox(a, b, atol = 1e-2) ? "≈" : "≉" |
|||
b = P(d) |
|||
@printf "%d: %.5f %s %.5f \n" d a comp(a, b) b |
|||
end |
|||
end |
|||
benford(fib(1000))</syntaxhighlight> |
|||
{{Out}} |
{{Out}} |
||
<pre> 413.400 μs (6695 allocations: 337.42 KiB) |
|||
<pre>julia> benford([fib(big(n)) for n = 1:1000]) |
|||
9x3 Array{Number,2}: |
|||
d Freq(d) P(d) |
|||
1 0.301 0.30103 |
|||
1: 0.30100 ≈ 0.30103 |
|||
2: 0.17700 ≈ 0.17609 |
|||
3: 0.12500 ≈ 0.12494 |
|||
4: 0.09600 ≈ 0.09691 |
|||
5: 0.08000 ≈ 0.07918 |
|||
6: 0.06700 ≈ 0.06695 |
|||
7: 0.05600 ≈ 0.05799 |
|||
8: 0.05300 ≈ 0.05115 |
|||
9: 0.04500 ≈ 0.04576 |
|||
</pre> |
</pre> |
||
=={{header|Kotlin}}== |
=={{header|Kotlin}}== |
||
<syntaxhighlight lang="scala">import java.math.BigInteger |
<syntaxhighlight lang="scala">import java.math.BigInteger |
||