## Abstract

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.

## Keywords

Maximum entropy problem‎ ‎Nonlinear optimization‎ ‎Lagrange multipliers method‎ ‎Linear programming‎.

## Article Details

How to Cite
Nikooravesh, Z., & Tayyebi, J. (2020). A linear programming-based approach to estimate discrete probability functions with given quantiles. Pakistan Journal of Statistics and Operation Research, 16(4), 839-849. https://doi.org/10.18187/pjsor.v16i4.2978

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