负二项分布随机变量和尾概率的界

Tail Probability Bound of Sums of Random Variables with Negative Binomial Distribution

研究了服从不同负二项分布的随机变量和尾概率的界。首先在服从不同负二项分布独立随机变量条件下,利用负二项分布概率母函数和Markov不等式得到了一个随机变量和尾概率的界,并对所求得的界进行改进,获得一个更加精确的界;其次在服从负二项分布的条件下,通过添加相依关系,得到了关于负相依随机变量和尾概率的界。

This paper studied the bounds of the tail probability of the sum of independent random variables with different negative binomial distributions.Firstly,under the condition of independent random variables with different negative binomial distributions,we used the probability generation function of the negative binomial distribution and Markov inequality to obtain tail probability bounds on the sum of random variables,which was improved to obtain a more accurate bound.Secondly,we obtained some bounds for the tail probability of the sum of negative dependent random variables by adding dependence relations under the condition of obeying the negative binomial distribution.