Application method of barrier functions in the problem of estimating the probability density of the parameterized approximations

The methods of obtaining a parameterized density function with a limited number of data. The solution of this problem by minimizing the functional. In the method of the barrier function minimization problem with inequality constraints reduced to solving a sequence of unconstrained minimization problems. The advantage of this approach lies in the number of restrictions is independent of the order of the polynomial. Practical implementation of the minimization of the above causes functional choice of basis functions and the required order of polynomials approximating the probability density function.