3.5.2.3 boxcox

1 Description
2 Syntax
3 Parameter
4 Return
5 Example
6 See Also

Description

This function takes a positive vector and transforms it into approximately normal distributed one by using Box-Cox power transformation method. The Box-Cox transform is formulated as following:

\[ Y'=\left\{ \begin{array}{ll} Y^\lambda&\lambda \neq 0\cr \ln(Y)&\lambda = 0 \end{array} \right. \]

Syntax

vector boxcox(vector vd[, double lambda, int options, int period])

Parameter

The input vector (column) to be transformed. vd must be positive dataset.

lambda

Optional. If specify a number, perform the Box-Cox transformation with the specified lambda. Default lambda is not a number (NANUM, i.e. “0/0”). In this case, the function will estimate the optimal lambda that maximizes the log-likelihood function before transformation, and lambda will be restricted in the range of [-5, 5].

options

Optinal. Specify the Box-Cox transformation method to use.

options = 0 (Default): use method similar to SciPy’s boxcox function;
options = 1: use the method in Statistical Process Control;
options =2: use the method in Time Series Analysis.

period

If options = 2, when Time Series Analysis method is used, specify period that determines the seasonal period of the original time series. period must be an integer not smaller than 2.

Return

Box-Cox power transformed vector (column).

Example

EX1

newbook;
col(A) = data(0.1, 1.1, 0.002);
col(B) = boxcox(col(A)); //output results similar to SciPy, with optimal lambda estimated by Origin
col(C) = boxcox(col(A),0/0,1); //use SPC method; lambda CANNOT be omitted, default "0/0" means estimating optimal lambda