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

作　　者：孙慧静 马启建 王丽英 SUN Huijing;MA Qijian;WANG Liying(School of Basic Sciences for Aviation,Naval Aviation University,Yantai 264001;Yantai Vocational College of Culture and Tourism,Yantai 264003,China)

机构地区：[1]海军航空大学航空基础学院,山东烟台264001 [2]烟台文化旅游职业学院,山东烟台264003

出　　处：《高等数学研究》2023年第4期1-5,105,共6页Studies in College Mathematics

基　　金：海军航空大学教育训练理论研究课题(13);海军航空大学“课程思政”专项研究立项课题(05).

摘　　要：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.

关 键 词：二项分布 负二项分布 泊松分布 条件分布 

分 类 号：G642[文化科学—高等教育学]