Federico Palacios González

A new condition to check the independence of random variables

This paper introduces a new criteria to check for independence of two random variables once their joint probability density function is known. The proposed procedure results in an easier way to verify stochastic independence compared to commonly used in statistical literature. Both continous and discrete variables are considered. In the former case it is assumed that the domain for one variable does not depend on the other.

Using generator function system to check independence of random variables

This study presents a criterion to determine the stochastic dependence or independence between the variables of a random vector or between two of its subvectors, either from the joint density function or from the generator function system for such a density. This criterion generalizes the condition discussed by HERRERIAS R., PALACIOS F. and CALLEJON J.(1997). There is a noteworthy simplicity of calculations, as the stochastic dependence or independence of random variables is seen as a consequence of the analytical dependence or independence in the generator function system.