Piecewise Distributions

Some density functions take a bipartite form. To illustrate, let us suppose is a continuous random variable, , with pdf

where . We enter this as:

This is known as the Inverse Triangular distribution, as is clear from a plot of , as illustrated in Fig.Ūd1.

Fig. 1: The Inverse Triangular pdf, when (bold), (plain), (dashed)

Here is the cdf, :

Note that the solution depends on whether or . Figure 2 plots the cdf at the same three values of used in Fig.1.

Fig. 2: The Inverse Triangular cdf, when (bold), (plain), (dashed)

mathStatica operates on bipartite distributions in the standard way. For instance, the mean is given by: