摘要
利用一类属于"δ型序列"并含有指数因子exp(-st)的概率密度函数,当在大于零的实数半区间上有且只有一个对应于随机变量众数的极值点横坐标时,将随机变量连续函数的数学期望用该函数的Laplace变换表出,从而导出一种基于δ型概率密度函数序列的数值Laplace反变换(NILT)算法基本框架,并把常用的Stehfest算法和Pos-tWidder算法统一至该框架之下.在此基础上,选择属于"δ型序列"的Gamma分布密度函数,提出一个此类NILT算法的新成员.
An algorithm framework of the numerical inversion of Laplace transforms （NILT）based on a class of probability density function ,which belongs to the sequence ofδ-type functions with exponential term exp （-st ）was presented .If the probability density function defined for all positive variables in the abscissa has and only has an extremum abscissa corresponding to the modal value of random variables ,the expectation of a continuous function of random variables can be expressed by the Laplace transform of this function .It is shown that the traditional Stehfest’s and Post-Widder′s NILT algorithm are two special cases of the proposed algorithm framework .Moreover ,an example using the δ-type Gamma distribution density function is given to demonstrate that the novel framework can help to develop new NILT algorithms .
出处
《电子学报》
EI
CAS
CSCD
北大核心
2013年第8期1474-1479,共6页
Acta Electronica Sinica
基金
国家自然科学基金(No.61201120)
关键词
数值Laplace反变换
广义函数
δ型序列
概率密度函数
numerical, in version of Laplace transforms
generalized function
sequence of δ-type functions
probability density function
