It relates to probability density functions by explaining how the distribution of these averages or sums tends to approach a specific shape: the normal distribution (bell curve).

The notion of probability density for a random function is not as straight-forward as in finite-dimensional cases. While a probability density function generally does not exist for functional data, we ...

The problem of estimating a probability density function has only recently begun to receive attention in the literature. Several authors [Rosenblatt (1956), Whittle (1958), Parzen (1962), and Watson ...