In your book, you might wish to mention the use of Bezier curves to empirically model arbitrarily complication cumulative probability distributions. They have several advantages (particularly for univariate distriutions):
The derivatives can be used (to easily) calculate probaility density function approximations
Fixed end points relating to a cumulative probability of 0 and a cumulative probability of 1.0
They make no assumptions about matching other (arbitrary) probability distributions
Hi
In your book, you might wish to mention the use of Bezier curves to empirically model arbitrarily complication cumulative probability distributions. They have several advantages (particularly for univariate distriutions):
The derivatives can be used (to easily) calculate probaility density function approximations
Fixed end points relating to a cumulative probability of 0 and a cumulative probability of 1.0
They make no assumptions about matching other (arbitrary) probability distributions
An article about them can be found at https://informs-sim.org/wsc93papers/1993_0052.pdf
Phil Troy