A probability density function (PDF) describes the likelihood of different outcomes for a continuous random variable.

A class of probability density estimates can be obtained by penalizing the likelihood by a functional which depends on the roughness of the logarithm of the density. The limiting case of the estimates ...

Probability Distribution (pdf) and Cumulative Distribution Function (cdf) The pdf is denoted by f (x) and the cdf is denoted by F (x). It is easy to see that f (x) defines a probability density ...

Asymptotic properties of estimates of a probability density function and its derivatives which use the kernel-method are studied. Some results on the rate of convergence of these estimates are ...

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 ...