oai:arXiv.org:2006.05458
sciences : mathématiques 2
2020
9/26/2023
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 $\delta$-records in the LDM, defined as observations which are greater than all previous observations, plus a fixed real quantity $\delta$.
We give analytical properties of the probability of $\delta$-records and study the correlation between $\delta$-record events.
We also analyse the asymptotic behaviour of the number of $\delta$-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.
;Comment: 30 pages, 12 figures
Gouet, Raúl,Lafuente, Miguel,López, F. Javier,Sanz, Gerardo, 2020, Exact and asymptotic properties of $\delta$-records in the linear drift model