广义边缘密度函数相关理论及应用

对二维连续型随机变量的联合密度函数,在一定要求下变上限积分得到新函数,依据密度函数性质进行规范化,从而构造出一个广义的边缘密度函数.分析该边缘密度函数广义形式与通常形式之间的关系,探讨密度函数广义形式下的多个性质.针对具体的广义形式,得出了多个新结果,并将密度函数广义形式推广到n维,最后讨论了这一广义形式在舍选抽样中的应用.

Relative theory of general marginal density function and its application

For the joint density function of 2-D continuous random variables,a new function can be obtained by upper limit-variable integral,and then,by normalization of the new function according to the property of density functions,a general marginal density function was constructed.The relationship between the general form and the conventional form of the density function was analyzed,and the properties of the density function with the general form were discussed.Furthermore,some new conclusions were drawn for a particular general form,and the general form was extended to the n-dimensional general marginal density function.Finally,the application of the general form to acceptance-rejection sampling was discussed.