兰州大学机构库 >数学与统计学院
基于记录值的贝叶斯预测
Alternative TitleBayesian prediction base on record values
程小宝
Thesis Advisor陈进源
2016-05-15
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword贝叶斯预测 记录值 指数分布 逆指数分布
Abstract记录值是某个特定时间段内的随机变量,在日常生活中随处可见,例如运动会的成绩、降雨量、气象温度、河流水位等等。所以对记录值的分析有着深远的现实意义。本文考虑基于上、下记录数据的贝叶斯预测问题,而且阐述了上下记录值的微妙差异。首先考虑记录值数据服从一般形式的参数分布模型,这种分布形式包含其他常见的分布,例如指数分布,威布尔分布等。在先验分布也是具有一般形式的情形下,我们推导了下一记录值在平方损失下的贝叶斯预测公式。接下来,为了论证这一结论,在上记录值条件下,我们具体推导了指数分布的记录值点预测值和区间预测;在下记录值中,通过不同的参数设置分别呈现了逆指数分布、逆威布尔分布的预测估计。最后用数据模拟验证了我们的预测方法并应用到一个真实数据例子,得到了很好的预测效果。
Other AbstractRecord value is a random variable for a specific time. Application of record values can be seen everywhere in daily life.Such as sports records,records of meteorological rainfall records,meteorological temperature records, flood levels of the river. So it is profound practical significance to analyse record values. This paper mainly we consider Bayesian prediction base on the upper and lower recorded data, and present a subtle difference between the upper and lower record values. First, we consider record data to obey the general form of the parameter distribution model, this general distribution form include other common distributions, such as exponential distribution, Weibull distribution and so on. In the case of the prior distribution is a general form, we derive the next record value under the square loss Bayesian forecasting formula. Next, in order to prove the conclusion, we detailed derive Exponential(θ) distribution point of prediction and interval prediction under the condition of record value; on the lower record value, through different parameter settings show the Inverse Exponential distribution, Inverse Weibull distribution point of prediction and interval prediction. Finally, we use the data simulation to verify our prediction method, and apply it to real data examples, and get a good prediction effect.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/225157
Collection数学与统计学院
Recommended Citation
GB/T 7714
程小宝. 基于记录值的贝叶斯预测[D]. 兰州. 兰州大学,2016.
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