A weighted estimator of the rate parameter of exponential-like distributions based on delta-records

M. Alcalde Navarro, R. Gouet Bañares, M. Lafuente Blasco, F. J. López Lorente, G. Sanz Sáiz

In Gouet et al. (2012) (DOI: https://doi.org/10.1007/s11749-011-0242-6), a maximum likelihood estimator (MLE) based on delta-records was proposed for the rate parameter of an exponential distribution. To extend this approach to the broader class of exponential-like distributions, we introduce a weighted version that places greater emphasis on the largest records and their associated near-records through an increasing sequence of weights. Using classical results on weighted laws of large numbers and central limit theorems, we establish weak and strong consistency, as well as asymptotic normality, under suitable assumptions on the weights and mild conditions on the parent distribution. Simulation results show that the proposed weighted estimator outperforms other estimators based on records in the literature when applied to exponential-like distributions other than the exponential law.

Keywords: Exponential-like distributions, records, delta-records, maximum likelihood estimation

GT Procesos Estocásticos y sus Aplicaciones I
September 2, 2026  11:20 AM
Aula 26

M. Lafuente Blasco, M. Alcalde Navarro, F. J. López Lorente, G. Sanz Sáiz

J. A. Vega Coso

J. Vives Santa-Eulalia