## Afrika Statistika

### A Central limit Theorem of dependent sums of standard exponential functionals motivated by extreme value theory

#### Abstract

Consider the following demimartingale \begin{equation*} \sum_{j=1}^{k-1}f(j)(\exp (-\gamma \sum_{h=j+1}^{k-1}E_{h}/h)-\exp (-\gamma \sum_{h=j}^{k-1}E_{h}/h)), \end{equation*} where $E_{1},E_{2},...$ are independent standard exponential random variables, $\gamma>0$, $k$ is a positive integer and $f(j)$ is an increasing function of the integer $j\geq1$. We find general conditions under which the central limit theorem (CLT) holds and next apply the results to find the asymptotic behavior of the functional Hill within the Extreme Value Theory (EVT) field. This results show a new trend for the central limit theorem issue for non-stationary sequences of associated variables.

#### Article information

Source
Afr. Stat., Volume 13, Number 3 (2018), 1795-1822.

Dates
First available in Project Euclid: 12 December 2018

https://projecteuclid.org/euclid.as/1544583716

Digital Object Identifier
doi:10.16929/as/1795.134

Mathematical Reviews number (MathSciNet)
MR3887184

Zentralblatt MATH identifier
07003217

#### Citation

Lo, Gane Samb; Fall, Adja Mbarka; Sangaré, Harouna. A Central limit Theorem of dependent sums of standard exponential functionals motivated by extreme value theory. Afr. Stat. 13 (2018), no. 3, 1795--1822. doi:10.16929/as/1795.134. https://projecteuclid.org/euclid.as/1544583716