Transformation of Random Variables
- Transform samples from one arbitrary distribution to another with a function
- Given random variable
drawn from some PDF . - Why the function
must be one-to-one? - Why the derivative of the transformation function
must be greater or equal to ? and therefore
- Why the derivative of the transformation function
- The relation
is a generalization of the inverse transform sampling since when is uniform random variable from , - Multiple dimensions
is the absolute value of the determinant of T’s Jacobian matrix where are defined by .