In practice this may be difficult to estimate as the density function is usually unknown.

In the details to follow, we show that this approach leads to a reasonable estimate of the underlying density function.

The goal is to turn this quantity p into the classical density function in phase space.

This will be made clearer by plots of the estimated density functions.

Elliptical distributions can also be defined in terms of their density functions.

This needs to be the case, because the density function needs to be 1.

For several of these cases, the maximum value of the density function occurs at one or both ends.

The reciprocal distribution has a density function of the form.

In other words, the product of their independent density functions does not adequately describe the real situation.

Methods of the first class model conditional density functions .