This package provides an implementation of Box Cox transformation. See Wikipedia - Power Transform for more information.
] add BoxCoxTrans
The simplest way is to just call the transform function with an array of numbers.
julia> using Distributions, UnicodePlots, BoxCoxTrans
julia> x = rand(Gamma(2,2), 10000) .+ 1;
julia> histogram(x)
┌──────────────────────────────────────────┐
(0.0,2.0] │▇▇▇▇▇▇▇▇ 852 │
(2.0,4.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 3554 │
(4.0,6.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 2655 │
(6.0,8.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1524 │
(8.0,10.0] │▇▇▇▇▇▇▇▇ 798 │
(10.0,12.0] │▇▇▇ 316 │
(12.0,14.0] │▇▇ 170 │
(14.0,16.0] │▇ 76 │
(16.0,18.0] │ 35 │
(18.0,20.0] │ 14 │
(20.0,22.0] │ 5 │
(22.0,24.0] │ 1 │
└──────────────────────────────────────────┘
julia> histogram(BoxCoxTrans.transform(x))
┌────────────────────────────────────────┐
(0.0,0.2] │▇▇ 64 │
(0.2,0.4] │▇▇▇▇ 166 │
(0.4,0.6] │▇▇▇▇▇▇▇▇▇▇ 386 │
(0.6,0.8] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 559 │
(0.8,1.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 887 │
(1.0,1.2] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1091 │
(1.2,1.4] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1257 │
(1.4,1.6] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1298 │
(1.6,1.8] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1281 │
(1.8,2.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1103 │
(2.0,2.2] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 877 │
(2.2,2.4] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 541 │
(2.4,2.6] │▇▇▇▇▇▇▇ 272 │
(2.6,2.8] │▇▇▇▇ 153 │
(2.8,3.0] │▇ 50 │
(3.0,3.2] │ 14 │
(3.2,3.4] │ 1 │
└────────────────────────────────────────┘
You can examine the power transform parameter (λ) derived by the program:
julia> BoxCoxTrans.lambda(x).value
0.013544484565969775
You can transfrom the data using your own λ:
julia> histogram(BoxCoxTrans.transform(x, 0.01))
┌────────────────────────────────────────┐
(0.0,0.2] │▇▇ 64 │
(0.2,0.4] │▇▇▇▇ 166 │
(0.4,0.6] │▇▇▇▇▇▇▇▇▇▇ 386 │
(0.6,0.8] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 563 │
(0.8,1.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 894 │
(1.0,1.2] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1094 │
(1.2,1.4] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1261 │
(1.4,1.6] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1302 │
(1.6,1.8] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1289 │
(1.8,2.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1111 │
(2.0,2.2] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 868 │
(2.2,2.4] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 534 │
(2.4,2.6] │▇▇▇▇▇▇▇ 268 │
(2.6,2.8] │▇▇▇▇ 142 │
(2.8,3.0] │▇ 47 │
(3.0,3.2] │ 11 │
└────────────────────────────────────────┘
There's an option to scale the results by the geometric mean.
julia> histogram(BoxCoxTrans.transform(x; scaled = true))
┌────────────────────────────────────────┐
(0.0,1.0] │▇▇ 81 │
(1.0,2.0] │▇▇▇▇▇▇ 258 │
(2.0,3.0] │▇▇▇▇▇▇▇▇▇▇▇▇ 540 │
(3.0,4.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 868 │
(4.0,5.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1234 │
(5.0,6.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1467 │
(6.0,7.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1521 │
(7.0,8.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1488 │
(8.0,9.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 1133 │
(9.0,10.0] │▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇▇ 806 │
(10.0,11.0] │▇▇▇▇▇▇▇▇ 359 │
(11.0,12.0] │▇▇▇▇ 188 │
(12.0,13.0] │▇ 50 │
(13.0,14.0] │ 7 │
└────────────────────────────────────────┘