论文标题
线性漂移模型中$δ$ - 记录的精确和渐近性特性
Exact and asymptotic properties of $δ$-records in the linear drift model
论文作者
论文摘要
由于在几个领域的应用，对线性漂移模型（LDM）中记录的研究最近引起了很多关注。在本文中，我们研究了LDM中的$δ$ - 记录，定义为观测值，其比以前的观测值大，再加上固定的实际数量$δ$。我们提供$δ$ - 记录的概率的分析性能，并研究$δ$ - 记录事件之间的相关性。我们还分析了第一个$ n $观测值之间$δ$ - 记录数的渐近行为，并为高斯分布提供了收敛条件。由于我们的结果，我们解决了J. STAT中提出的猜想。机械。 2010年，P10013，关于LDM中的记录总数为负漂移。还提供了针对特定分布的示例，例如Gumbel或Pareto。我们用西班牙的夏季温度的真实数据集说明了我们的结果，在西班牙，LDM与全球温暖现象一致。
The study of records in the Linear Drift Model (LDM) has attracted much attention recently due to applications in several fields. In the present paper we study $δ$-records in the LDM, defined as observations which are greater than all previous observations, plus a fixed real quantity $δ$. We give analytical properties of the probability of $δ$-records and study the correlation between $δ$-record events. We also analyse the asymptotic behaviour of the number of $δ$-records among the first $n$ observations and give conditions for convergence to the Gaussian distribution. As a consequence of our results, we solve a conjecture posed in J. Stat. Mech. 2010, P10013, regarding the total number of records in a LDM with negative drift. Examples of application to particular distributions, such as Gumbel or Pareto are also provided. We illustrate our results with a real data set of summer temperatures in Spain, where the LDM is consistent with the global-warming phenomenon.
