AFRIKA STATISTIKA

# Théorie des Probabilités et Statistiques Mathématiques et domaines connexes

## Journal contents / Contenu du Journal

### Volume 13, Numéro 3, Année 2018

Gane Samb LO,Adja Mbarka FALL,Harouna SANGARE,
A Central limit Theorem of dependent sums of standard exponential functionals motivated by extreme value theory, pp. 1795-1822
DOI : http://dx.doi.org/10.16929/as/1795.134
ABSTRACT
ENGLISH 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

FRANCAIS 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 $$j\geq 1$$. 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
Citer cet article
Gane Samb LO,Adja Mbarka FALL,Harouna SANGARE, (2018). A Central limit Theorem of dependent sums of standard exponential functionals motivated by extreme value theory. Afrika Statistika . Volume 13(3), pp 1795-1822
Doi : http://dx.doi.org/10.16929/as/1795.134

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