Exact and asymptotic properties of δ-records in the linear drift model

Autor:	Gerardo Sanz, F. J. López, M. Lafuente, Raúl Gouet Bañares
Rok vydání:	2020
Předmět:	Statistics and Probability Delta Exact results Stochastic process Applied mathematics Mathematics - Statistics Theory Statistical and Nonlinear Physics Linear drift Statistics Probability and Uncertainty Extreme value theory Mathematics - Probability Mathematics
Zdroj:	Journal of Statistical Mechanics: Theory and Experiment. 2020:103201
ISSN:	1742-5468
Popis:	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
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::eef4d756b408e020f8c145e66b6dc12f https://doi.org/10.1088/1742-5468/abb4dc Zobrazit plný text záznamu