A new calculation algorithm for quantile function with application to headway distribution

The maximum entropy approach is a flexible and powerful tool for probability curve approximation. This paper presents an effective algorithm for estimating parameters of the maximum entropy quantile function subject to probability-weighted moments constraints. The algorithm is proposed by utilizing optimization method to estimate parameters that would lead to the best-fit quantile function. The central idea of the algorithm is to transfer the problem of finding roots of equations to the problem of equivalent optimization. The numerical examples presented in the paper illustrate the effectiveness of the proposed algorithm.