A linear programming-based approach to estimate discrete probability functions with given quantiles

The aim of this paper is to estimate probability distribution functions with maximum entropy and known quantiles. The paper formulates the problem as a nonlinear optimization problem, and converts it into a system of nonlinear equations by Lagrange multipliers method. Finally, an efficient method is proposed to obtain a solution of the nonlinear system. The method needs to solve a linear programming problem in each iteration. Since linear programming problems can be solved in a reasonable time, our proposed method is faster than generic methods of solving nonlinear programming problems. Several computational experiment are provided to demonstrate the performance and validation of our proposed method.