基于流图模型的矩生成函数的计算及鞍点逼近

Calculation and Saddlepoint Approximation of Moment Generating Functions Based on Flow-graph Models

介绍了流图模型的矩生成函数的计算及其鞍点逼近问题.给出了矩生成函数的另一种推导方法并利用Maple计算相关方程.利用矩模拟的方法进行参数估计,得到了概率密度函数、生存函数和危险函数的鞍点逼近.结果表明鞍点逼近算法能较好地捕捉实际函数曲线的动态演变,且达到了估计误差小和逼近精度高的预期目标.

This paper concentrates on the calculation and saddlepoint approximation of moment generating functions based on flow - graph models. First, an alternative method for deriving moment generating function is presented and the corresponding equations are solved by the Maple software. Then moment simulation method applies for parameter estimation and saddlepoint approximations of density functions, survival functions and hazard functions are obtained, respectively. The results show that the saddlepoint approximation algorithm could capture the dynamic evolution of real function curves, and the estimate error and approximation accuracy are within our expectation.