【摘要】 随机变量概率分布参数的信度函数可采用信仰分布的方法生成,但目前的生成方法存在信仰分布不一致的现象,其主要原因是采用了不同的联合信任密度函数.根据分布参数信仰分布与样本观测值概率密度之间的关系,提出信度函数生成的基本思想和极大似然法、贝叶斯法,并将其应用于正态分布参数和分位值信度函数的建立.两种方法具有更好的理论基础,对分布参数的推断均源于同一联合信任密度函数,可明确考虑其他分布参数的信息,其中贝叶斯法的推断结果与经典统计学中区间估计法的相同,较极大似然法的结果更为有利,一般应以贝叶斯法作为信度函数生成的主要方法.更多还原

【Abstract】 The method with which to generate belief function of the probability distributed parameters of random variable is similar to the one for generating fiducial distribution. However,the fiducial distribution of the same distribution parameter shows differences by present method.The basic reason is to adopt different joint belief density function. Based on the relations between fiducial distribution of distributed parameters and probability density of sample observation values,the paper proposed the essential ideas and the maximum likelihood method and Bayesian method,and then established belief function of normal distributed parameters and fractiles. Based on a reliable theory,two methods are used to infer distributed parameters originated from the same joint belief density function,taking into account of the other distributed parameter’s information.With the Bayesian method the same results with the interval estimation of classical statistics can be achieved,which is more reasonable than maximum likelihood method. Bayesian method is a basic method for generating belief function in general conditions.更多还原