Subindependence

In probability theory and statistics, subindependence is a weak form of independence.
Two random variables X and Y are said to be subindependent if the characteristic function of their sum is equal to the product of their marginal characteristic functions. Symbolically:
This is a weakening of the concept of independence of random variables, i.e. if two random variables are independent then they are subindependent, but not conversely. If two random variables are subindependent, and if their covariance exists, then they are uncorrelated.
Subindependence has some peculiar properties: for example, there exist random variables and that are subindependent, but and are not subindependent when and therefore and are not independent.
One instance of subindependence is when a random variable is Cauchy with location and scale and another random variable, the antithesis of independence. Then is also Cauchy but with scale. The characteristic function of either or in is then, and the characteristic function of is.