  In this paper, we will discuss how to generalize nonparametric density
estimators to MLE parametric estimators. Basing on the Parzen window theory and
using the advantages of probability amplitude of quantum theory, we model a
nonlinear optimization problem and it is very difficult, if not impossible, to
solve the problem. A constructive procedure for solving the nonlinear
programming problem is studied. Though it seems to be very complicated, the
approach of this paper is simple and comprehensive. More precisely, the lemmas,
the theorems and their proofs serve the purpose for mathematical rigor and
practical computation. Instead of using techniques and terminologies of
advanced mathematics, we use the popular techniques and terminologies of
elementary calculus. From the numerical results of the paper by Y. --S. Tsai et
al. [7], it shows that a new approach of density estimation, super-parametric
density estimation, is established completely. Strictly speaking, the work of
the paper is not confined in the category of statistics. It could be classified
into nonlinear analysis such as optimization on linear space, or manifold, and
the algorithm of computer science.
