Function - Array Transform Box-Cox

// This source code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © RicardoSantos

//@version=5
indicator(title='Function - Array Transform Box-Cox')
//      https://www.statology.org/box-cox-transformation-excel/
//      https://www.geeksforgeeks.org/box-cox-transformation-using-python/
//      https://github.com/business-science/timetk/blob/master/R/vec-box_cox.R
//      https://frost-lee.github.io/box-cox-linear-model/
//      https://otexts.com/fpp2/transformations.html
//

array_transform_boxcox_regular(_sample, _lambda) =>
    int _size = array.size(id=_sample)
    if _size > 0
        _X = array.copy(id=_sample)
        for _i = 0 to _size - 1 by 1
            _xi = array.get(id=_X, index=_i)
            if _lambda == 0
                array.set(id=_X, index=_i, value=math.log(_xi))
            else
                array.set(id=_X, index=_i, value=math.sign(_xi) * (math.pow(math.abs(_xi), _lambda) - 1) / _lambda)
        _X

array_transform_boxcox_inverse(_sample, _lambda) =>
    int _size = array.size(id=_sample)
    if _size > 0
        _X = array.copy(id=_sample)
        for _i = 0 to _size - 1 by 1
            _xi = array.get(id=_X, index=_i)
            if _lambda == 0
                array.set(id=_X, index=_i, value=math.exp(_xi))
            else
                _xe = _lambda * _xi + 1.0
                array.set(id=_X, index=_i, value=math.sign(_xe) * math.pow(math.abs(_xe), 1.0 / _lambda))
        _X

lambda = input(0.5225)
sample_data = array.from(4.0, 5.0, 2.0, 3.0, 3.0, 2.0, 2.0, 3.0, 2.0, 3.0, 4.0, 3.0, 8.0, 6.0)
Y = array_transform_boxcox_regular(sample_data, lambda)
iY = array_transform_boxcox_inverse(Y, lambda)
var label la = label.new(bar_index, 0.0, '')
label.set_xy(la, bar_index, 0.0)
label.set_text(la, 'sample: ' + str.tostring(sample_data) + '\ninverse: ' + str.tostring(iY) + '\nregular: ' + str.tostring(Y))
plot(array.get(Y, bar_index % array.size(Y)))