Nonlinear transformation of random variables

1. What is nonlinear transformation?
2. What is the transformation of random variables?
3. What are the most common non-linear transformations?

What is nonlinear transformation?

A nonlinear transformation changes (increases or decreases) linear relationships between variables and, thus, changes the correlation between variables. Examples of a nonlinear transformation of variable x would be taking the square root of x or the reciprocal of x.

What is the transformation of random variables?

The transformation y=a+Bx maps Rn one-to-one and onto Rn. The inverse transformation is x=B−1(y−a). The Jacobian of the inverse transformation is the constant function det(B−1)=1/det(B). The result now follows from the multivariate change of variables theorem.

What are the most common non-linear transformations?

Types of Transformations

The most common ways to transform nonlinear data is by using one of these models: Power model. Logarithm model. Square root model.