| 非齐次负二项随机变量卷积的若干结果 |
| Alternative Title | Some Results on Convolutions of Heterogeneous Negative Binomial Random Variables
|
| 边宁 |
| Thesis Advisor | 赵鹏
|
| 2013-06-26
|
| Degree Grantor | 兰州大学
|
| Place of Conferral | 兰州
|
| Degree Name | 硕士
|
| Keyword | 似然比序
失效率序
平均剩余寿命序
熵
负二项卷积
|
| Abstract | 独立随机变量的卷积问题经常出现在应用概率、可靠性理论、寿命检验、精算学以及运筹学等很多应用领域中。当卷积中的随机变量具有不同分布时，卷积的分布理论就会变得异常复杂，此种情形下卷积的随机比较问题引起了广泛的关注。以往的的文献中有很多关于指数，伽马，几何随机变量卷积的随机比较的结果。负二项分布在统计学中有着广泛的应用，被普遍应用于点计数据以及贝叶斯推断中。鉴于负二项卷积分布形式的复杂性，负二项随机变量卷积的随机比较问题仍未在文献中见到相关结果。本文利用负二项分布与伽马分布的内在结构关系，将伽马卷积的随机比较结果推广到负二项卷积中，研究了负二项随机变量卷积的似然比序，失效率序，平均剩余寿命序。同时，本文研究了负二项随机变量的熵比较问题。 |
| Other Abstract | Convolutions of independent random variables often arise in a natural way in many applied areas including applied probability, reliability theory, life testing，actuarial science, and operations research. Negative binomial distribution is used commonly to model count data, especially in Bayesian inference. There are very few results on convolutions of heterogeneous negative binomial random variables due to the complexity of the distribution theory. In this thesis, we apply the results on convolutions of heterogeneous gamma random variables to the situation of negative binomial random variables by a special relationship between their distributions. We study the likelihood ratio order, hazard rate order, mean residual life order between convolutions of two heterogeneous negative binomial sets of variables wherein they have differing parameters. The variability between convolutions of two heterogeneous negative binomial sets of variables are also compared in terms of entropy. |
| URL | 查看原文
|
| Language | 中文
|
| Document Type | 学位论文
|
| Identifier | https://ir.lzu.edu.cn/handle/262010/225462
|
| Collection | 数学与统计学院
|
Recommended Citation
GB/T 7714 |
边宁. 非齐次负二项随机变量卷积的若干结果[D]. 兰州. 兰州大学,2013.
|
Items in the repository are protected by copyright, with all rights reserved, unless otherwise indicated.
