Academic Journal of Computing & Information Science, 2022, 5(12); doi: 10.25236/AJCIS.2022.051207.
Sichuan Minzu College, Kangding, Sichuan, 626001, China
Random variables are the most fundamental concept in probability theory and mathematical statistics. Each random variable can have a distribution, different random variables can have different distributions, and different random variables can have the same distribution. There are many random variables, and there are many distributions that can be formed, but there are not many commonly used distributions. In general probability theory and mathematical statistics textbooks, each distribution is explained separately, and the relationship between distributions is occasionally discussed, and there is no detailed description. Establishing the correspondence between distributions plays an important role in mastering the theory and relationship of common distributions. This paper studies the relationship between distributions, and establishes some common distribution diagrams on the basis of distribution relationships, so as to illustrate the connections between some distributions with distribution diagrams.
random variables, probability distributions, discrete distributions, continuous distributions, correspondence
Xiaobo Wen. Analysis of Relationships between Common Distributions Based on Computing Science. Academic Journal of Computing & Information Science (2022), Vol. 5, Issue 12: 47-54. https://doi.org/10.25236/AJCIS.2022.051207.
 Zhang Dan. The relationship between several common probability and statistics distributions [J]. Journal of Xianyang Normal University,2019,2(32):51-54.
 Gao Xiancai, Shan Xuehong. Study on gamma probability distribution properties [J]. Journal of Zaozhuang University.2018,2(35):26-29.
 Zhu Fang. WANG Hui. Research on the relationship between exponential distribution and other distributions based on MGF[J]. Journal of Suihua University,2018,11,144-145.
 Zhao Tianyu. Research on probability distribution of common discrete random variables based on parent function [J]. Journal of Yangtze University (Natural Science Edition), 2013, 10,(28):1-4.
 Wang Lifang. A discussion on the relationship between binomial distribution, Poisson distribution and exponential distribution. Journal of Henan University of Education (Natural Science Edition), 2013, 2(22):16-18.
 Jing Yingchuan, Luo Chun, Chen Xueping. There are often continuous distribution properties summary and its relationship. Journal of Shanghai Institute of Technology (Natural Science Edition), 2009, 4(9):314-318.
 Hou Wen. The relationships among the commonly used probability distributions. Journal of Liaoning Normal University (Natural Science Edition), 2005, 4(28):503-505.
 Tao Huiqiang. Research on the relationship between commonly used probability distributions and its application [J].Journal of Huaihua University.2011,5(30):75-78.
 Mao Shisong, Cheng Yiming, Pu Xiaolong. (2011) Course of Probability Theory and Mathematical Statistics [M]. Beijing: Higher Education Press.