最大熵分位值估计及其对偶型优化解法

针对经典最大熵分位值估计中拉格朗日系数计算目前存在高度非线性、计算结果精度不高或有时难以收敛等问题,提出了一种对偶型 逐次寻优的方法.基于拉格朗日对偶法,推导建立了含有拉格朗日系数优化函数的对偶表达式；在此基础上,基于样本的概率权重矩约束,提出了逐次寻优算法.针对几种常见的概率分布类型和一种较为复杂的概率分布类型,采用对偶型最大熵方法和经典最大熵方法对其概率累积函数和分位值进行计算对比分析表明:对偶型最大熵分位值估计不仅具有非线性程度低、形式简单,而且对偶型 逐次寻优的方法具有比较高的计算精度,优化迭代的收敛性好等特点. 

Maximum entropy quantile estimation and dual optimization method

Based on high nonlinearity, low computational accuracy, or hard convergence of Lagrangian calculation in the classic maximum entropy quantile function, a new method called dual sequential updating method was proposed. Dual expression of optimization function was established on the basis of Lagrangian dual approach. Further sequential updating method was proposed based on the constraint by the probability weighted moments. After analyzing several common distributions and a complex distribution by dual maximum entropy quantile function and classic maximum entropy quantile function, result showed that,dual maximum entropy quantile function had advantage of low nonlinearity and simple form, and dual sequential updating method had good computational accuracy and optimization convergence.