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| 摘要: |
| 本文研究了在伯努利试验下的收集问题, 利用混料格子点集的理论,推导出了多项几何分布的概率函数. 在伯努利试验中,如果假设各种试验结果发生的概率都相等,进一步提出了均匀多项几何分布.我们得到了两类分布的概率函数以及期望与方差,通过模拟验证了这两类分布与正态分布的差异,并由模拟结果建立关于概率与试验次数的多项式回归模型, 使用该模型可以有效的简化计算. |
| 关键词: 多项分布 几何分布 概率函数 |
| DOI： |
| 分类号:O211 |
| 基金项目:Supported by Science and Technology Fund for Basic Research of Guizhou Province ([2020]1Y010); National Nature Sciences Foundation of China (NSFC 11901260). |
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| THE MULTINOMIAL GEOMETRIC DISTRIBUTION |
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LI Guang-hui,LI Jun-peng,ZHANG Chong-qi
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| Abstract: |
| In this paper, we studied the collection problem under Bernoulli’s trials and derived a probability function of the multinomial geometric distribution by using the theory of mixture lattice point sets. Further, we proposed a uniform multinomial geometric distribution when the probabilities of each of the trial outcomes are assumed to be equal in Bernoulli’s trial. Moreover, we obtained the probability functions, the expectation, and the variance of the two types of distributions, and verified the differences between these two types of distributions and the normal distribution by means of simulations. Finally, we developed a polynomial regression model on the probability and the number of trials from the simulation results, which can be used to simplify the calculation effectively. |
| Key words: multinomial distribution geometric distribution probability function |
