papaya
Class Linear.BoxCox

java.lang.Object
  papaya.Linear.BoxCox

Enclosing class:

Linear

public static class Linear.BoxCox
extends Object

Contains methods related to the Box-Cox transformation of a data set; useful in determining the best transformation that will yield the best method for converting a monotonic, non-linear relationship between x and y into a linear one.

Reference:
Box, George E. P.; Cox, D. R. (1964). "An analysis of transformations". Journal of the Royal Statistical Society, Series B 26 (2): 211?252.
NIST/SEMATECH e-Handbook of Statistical Methods, EDA Section 1.3.3.6: Box-Cox Linearity Plots (The reader's digest version of the original.)

Method Summary

static float[]	correlation(float[] x, float[] y, float[] lambda) Performs the box-cox transformation on y for a sequence of λ and returns the array of linear correlation coefficients between the x and the box-cox transformed y.
static float[]	transform(float[] data, float lambda) Performs the box-cox transformation, returning the transformed data.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Detail

correlation

public static float[] correlation(float[] x,
                                  float[] y,
                                  float[] lambda)

Performs the box-cox transformation on y for a sequence of λ and returns the array of linear correlation coefficients between the x and the box-cox transformed y. at each value of λ . The value of λ corresponding to the maximum correlation (or minimum for negative correlation) is the optimal choice for λ such that the relationship between x and T(y) is linear.

Reference:
NIST/SEMATECH e-Handbook of Statistical Methods, EDA Section 1.3.3.6: Box-Cox Linearity Plots

Parameters:

x - the independent data array

y - the dependent data array

lambda - an array of lambda values

Returns:

the array containing the linear correlation coefficients, r.

transform

public static float[] transform(float[] data,
                                float lambda)

Performs the box-cox transformation, returning the transformed data. That is, it computes and returns

 y[i](λ) = (y[i]^λ-1) / λ if λ ≠ 0
 
 y[i](λ) = log(y[i])if λ = 0
 

Requirements: all elements of y are >0.

Parameters:

data - the data to be transformed

lambda - the lambda value

Returns:

the transformed data, or y(λ) above.