The main property of a discrete joint probability distribution can be stated as the sum of all non-zero probabilities is 1. The next line shows this as a formula. The marginal distribution of X can be ...

Density functions are nonnegative for all real numbers but greater than zero only at a finite or countably infinite number of points. Density functions are nonnegative for all real numbers and are ...

This is a preview. Log in through your library . Abstract The notion of probability density for a random function is not as straight-forward as in finite-dimensional cases. While a probability density ...

This is a preview. Log in through your library . Abstract Let x1, ⋯, xn be independent observations on a p-dimensional random variable X = (X1, ⋯, Xp) with absolutely continuous distribution function ...

After publication of an earlier version of this paper, we received feedback that there were several incorrect references to related methods in the literature. These errors are corrected in the current ...