概率分布收敛 convergence of probability distribution
- 给出了它的几个等价命题,同时还证明了独立随机变量和序列几乎处处收敛等价于依概率收敛,亦等价于依分布收敛。
This paper gaves its equivalent propositions and proves that a. s. convergence of independent random variables's sum variables is equivalent to its probability convergence, and equivalent to its weak convergence. - 摘要由随机变量序列几乎处处收敛可推出其依概率收敛,进而可推出其依分布收敛,可见判别几乎处处收敛的重要性。
Through almost sure convergence of random variables, the probability convergence can be derived; and further the weak convergence can be derived. - 证明了当保单数趋于无穷多时,平均损失变量按概率收敛于某一个随机变量,推导得到了该随机变量的近似分布函数。
It is proved that as the number of insured tends to infinity the average prospective loss random variable of this portfolio tends in probability to a certain random variable of which the approximate distribution function is derived.