Extremes, extremal index estimation, records, moment problem for the Pseudo-Lindley distribution and applications

TL;DR

This paper investigates the upper tail behavior of the Pseudo-Lindley distribution, analyzing extremal properties, estimators, and record values to enhance understanding of its tail characteristics and applications.

Contribution

It provides new insights into the tail behavior, asymptotic properties of estimators, and the moment problem for the Pseudo-Lindley distribution, which was previously less studied.

Findings

Asymptotic normality of the Hill estimator established

Behavior of record values analyzed and characterized

Results applicable to tail risk assessment and modeling

Abstract

The pseudo-Lindley distribution which was introduced in Zeghdoudi and Nedjar (2016) is studied with regards to its upper tail. In that regard, and when the underlying distribution function follows the Pseudo-Lindley law, we investigate the behavior of its values, the asymptotic normality of the Hill estimator and the double-indexed generalized Hill statistic process (Ngom and Lo), the asymptotic normality of the records values and the moment problem.