This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We succeeded in determining a subsequence which allows us to establish a convergence in law of the extremes of this type of random variable while passing by the determination of a speed of convergence. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type. These results will allow us to analyze, in a document, not only the convergence in moment of order of the other extremes of the random variables of geometric type but also the general asymptotic behavior of the extremes of a serie of random variables with integer value. This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We first made the case of the fact that the random variables of geometric type could be constructed from the random variables of exponential distribution and that they were not only integer variables but also that in general there were no sequences standards that allowed their extremes to converge. To do this, we first built a convergent ϕ(k) subsequence which we then used to define a geometric type Tϕ(k) subsequence of random variables. We have also proved the convergence in distribution of the extremes of the random variables Tϕ(k). We have also exhibited the resulting limit law. Finally, in this document, we have dealt with the multivariate case of random variables of geometric type. We considered two independent samples of random variables of geometric types. Using a copula of extreme values, in particular the logistic copula, we proposed a joint limit distribution of two independent samples of subsequences of geometric type random variables. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type.
| Published in | Applied and Computational Mathematics (Volume 10, Issue 6) |
| DOI | 10.11648/j.acm.20211006.12 |
| Page(s) | 138-145 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2021. Published by Science Publishing Group |
Asymptotic Convergence, Generalized Extreme Value Distribution, Exponantial and Geometric Distribution, Extreme Values Copulas
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APA Style
Frédéric Béré, Kpèbbèwèrè Cédric Somé, Remi Guillaume Bagré, Pierre Clovis Nitiéma. (2021). Asymptotic Behavior of Multivariate Extremes Geometric Type Random Variables. Applied and Computational Mathematics, 10(6), 138-145. https://doi.org/10.11648/j.acm.20211006.12
ACS Style
Frédéric Béré; Kpèbbèwèrè Cédric Somé; Remi Guillaume Bagré; Pierre Clovis Nitiéma. Asymptotic Behavior of Multivariate Extremes Geometric Type Random Variables. Appl. Comput. Math. 2021, 10(6), 138-145. doi: 10.11648/j.acm.20211006.12
AMA Style
Frédéric Béré, Kpèbbèwèrè Cédric Somé, Remi Guillaume Bagré, Pierre Clovis Nitiéma. Asymptotic Behavior of Multivariate Extremes Geometric Type Random Variables. Appl Comput Math. 2021;10(6):138-145. doi: 10.11648/j.acm.20211006.12
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author = {Frédéric Béré and Kpèbbèwèrè Cédric Somé and Remi Guillaume Bagré and Pierre Clovis Nitiéma},
title = {Asymptotic Behavior of Multivariate Extremes Geometric Type Random Variables},
journal = {Applied and Computational Mathematics},
volume = {10},
number = {6},
pages = {138-145},
doi = {10.11648/j.acm.20211006.12},
url = {https://doi.org/10.11648/j.acm.20211006.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211006.12},
abstract = {This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We succeeded in determining a subsequence which allows us to establish a convergence in law of the extremes of this type of random variable while passing by the determination of a speed of convergence. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type. These results will allow us to analyze, in a document, not only the convergence in moment of order of the other extremes of the random variables of geometric type but also the general asymptotic behavior of the extremes of a serie of random variables with integer value. This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We first made the case of the fact that the random variables of geometric type could be constructed from the random variables of exponential distribution and that they were not only integer variables but also that in general there were no sequences standards that allowed their extremes to converge. To do this, we first built a convergent ϕ(k) subsequence which we then used to define a geometric type Tϕ(k) subsequence of random variables. We have also proved the convergence in distribution of the extremes of the random variables Tϕ(k). We have also exhibited the resulting limit law. Finally, in this document, we have dealt with the multivariate case of random variables of geometric type. We considered two independent samples of random variables of geometric types. Using a copula of extreme values, in particular the logistic copula, we proposed a joint limit distribution of two independent samples of subsequences of geometric type random variables. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type.},
year = {2021}
}
TY - JOUR T1 - Asymptotic Behavior of Multivariate Extremes Geometric Type Random Variables AU - Frédéric Béré AU - Kpèbbèwèrè Cédric Somé AU - Remi Guillaume Bagré AU - Pierre Clovis Nitiéma Y1 - 2021/11/11 PY - 2021 N1 - https://doi.org/10.11648/j.acm.20211006.12 DO - 10.11648/j.acm.20211006.12 T2 - Applied and Computational Mathematics JF - Applied and Computational Mathematics JO - Applied and Computational Mathematics SP - 138 EP - 145 PB - Science Publishing Group SN - 2328-5613 UR - https://doi.org/10.11648/j.acm.20211006.12 AB - This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We succeeded in determining a subsequence which allows us to establish a convergence in law of the extremes of this type of random variable while passing by the determination of a speed of convergence. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type. These results will allow us to analyze, in a document, not only the convergence in moment of order of the other extremes of the random variables of geometric type but also the general asymptotic behavior of the extremes of a serie of random variables with integer value. This document was an opportunity for us to measure the contributions of researchers on the asymptotic behavior of the extremes random variables. Beyond the available results, we have proposed an analysis of the behavior of the extremes of random variables of geometric type. We first made the case of the fact that the random variables of geometric type could be constructed from the random variables of exponential distribution and that they were not only integer variables but also that in general there were no sequences standards that allowed their extremes to converge. To do this, we first built a convergent ϕ(k) subsequence which we then used to define a geometric type Tϕ(k) subsequence of random variables. We have also proved the convergence in distribution of the extremes of the random variables Tϕ(k). We have also exhibited the resulting limit law. Finally, in this document, we have dealt with the multivariate case of random variables of geometric type. We considered two independent samples of random variables of geometric types. Using a copula of extreme values, in particular the logistic copula, we proposed a joint limit distribution of two independent samples of subsequences of geometric type random variables. We then exposed the limited law which results from it then we called upon the copulas of the extreme values to propose a joint limited law for two independent samples of random variables of geometric type. VL - 10 IS - 6 ER -
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