与二项分布有关的概率分布之间关系注记

On Relations of Probability Distributions Related to Binomial Distribution

为揭示二项分布与其他分布之间的联系,从分布的产生背景出发,运用理论分析和数值计算并仿真模拟相结合的方法,解释或证明分布之间存在的“特殊和一般”关系、“极限”关系、“变换”关系以及“特殊情形下生成”的关系,并补充参考文献中没有或少有的证明过程.特别地,证明了负二项分布与二项分布之间存在的特殊变换关系以及以泊松分布为条件的泊松分布的条件分布为二项分布等结论.

In order to establish the relationships between binomial distribution and other distributions as well as normal distribution,starting from the background of distribution,design specific examples,and use the method of combining theoretical analysis with numerical calculation and simulation to explain or prove the relationships such as‘special and general’,the‘limit’,the‘transformation’and the‘generation under special circumstances’,and to supplement the proof methods that are not available or rare in the references.In particular,it is proved that there is a transformation relationship between negative binomial distribution and binomial distribution and that the conditional distribution of Poisson distribution with Poisson distribution as condition is the binomial distribution.