Exact and asymptotic properties of $\delta$-records in the linear drift model

Document detail

ID

oai:arXiv.org:2006.05458

Topic

Mathematics - Statistics Theory Mathematics - Probability

Author

Gouet, Raúl Lafuente, Miguel López, F. Javier Sanz, Gerardo

Year

2020

listing date

9/26/2023

Keywords

study observations $\delta$-records

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Abstract

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

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