Random noise and perturbation of copula with a copula induced noise

ABSTRACT

In this work, we propose an extension of the Irwin–Hall distribution to obtain the distribution of sum X + Y when the random variables X, Y are connected by a copula $C_{X,Y}$. Assuming that $C_{X,Y,Z}$ is the copula of random vector $(X,Y,Z)$, we then use the proposed distribution to study the perturbation of copula $C_{X+Z,Y}$. Theoretical results are illustrated by several examples.

KEYWORDS:

• Copula
• noise
• perturbation of copula
• Irwin–Hall distribution
• random vector
• measurement error

Acknowledgments

The work on this paper was supported by the grants APVV-18-0052 and VEGA 1/0006/19.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

The work on this paper was supported by the Agentúra na Podporu Výskumu a Vývoja [grant numbers APVV-18-0052 and VEGA 1/0006/19].

Notes on contributors

Ayyub Sheikhi

Ayyub Sheikhi received his Ph.D. from Shahid Bahonar Unversity, Kerman, Iran in 2012. From 2008 he has been a Member of the Faculty of mathematics, Department of Statistics, Shahid Bahonar Unversity, Kerman, Iran where he is currently an Assistant Professor. His intrests are Copula, Machin learning and Statistical Genetics. He also has obtained the second rank in statistical softwares in the First Iranian Statistical competition.

Fereshteh Arad

Fereshteh Arad Graduated from the department of statistics, Shahid Bahonar University of Kerman, Iran, with thesis topic ‘On the use of dependency measures in measurement error models’. During her bachelor's and master's degrees, she was one of the top students amd her research activities in 2019 caused her to introduced as a top researcher in department of statistics, Shahid Bahonar University of Kerman.

Radko Mesiar

Radko Mesiar received the Graduate degree from the Faculty of Mathematics and Physics and the Ph.D. degree with the thesis ‘Subadditive martingale processes’ from Comenius University, Bratislava, Slovakia, in 1974 and 1979, respectively. In 1996, he received the D.Sc. degree from the Academy of Sciences of the Czech Republic, Prague, Czech Republic. Since 1978, he has been a Member of the Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology (STU), Bratislava, where he is currently a Full Professor. In 1983, he became an Associate Professor and, in 1998, a full Professor. Since 1994, with small interruptions, he is a head of his department. In 1995, he became a Fellow Member of the Czech Academy of Sciences, Institute of Information and Automation, Praha, Czech Republic, and, in 2006, of IRAFM, University of Ostrava, Ostrava, Czech Republic. He is the coauthor of two influencial scientific monographs: Triangular Norms (Kluwer, Dordrecht, 2000) and Aggregation Functions (Cambridge, UK: Cambridge Univ. Press, 2009), and co-editor of ten edited volumes. He is the (co-)author of more than 300 papers in impacted WOS journals and about 200 other papers in WoS, where his h-index is now 43. His research interests include aggregation operators, measure and integral theory, uncertainty modelling, fuzzy sets and fuzzy logic, multicriteria decision support (including scintometric applications), copulas, triangular norms, and intelligent computing. Prof. Mesiar has been elected as a Fellow of the International Fuzzy Systems Association since 2011 and awarded as a brilliant scientist by EUSFLAT association in 2017. He is a Founder and Organizer of the FSTA, ISCAMI, ISAS, and AGOP international conferences. He is an area editor of distinguished journals Fuzzy Sets and Systems and Information Sciences, and member of editorial board of International Journal of Approximate Reasoning, International Journal of General Systems, Kybernetika, Iranian Journal of Fuzzy Systems, Axioms, and Granular Computing, among others.

Lucia Vavríková

Lucia Vavríková received her Ph.D. degree with the thesis ‘Transitive Preference Structures and Multicriteria Decision Making’ from Slovak University of Technology in Bratislava, Slovakia, under Prof. Radko Mesiar's Supervision. From 2011 she has been a Member of the Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology (STU), Bratislava, where she is currently an Assistant Professor. Her research interests are Multicriteria Decision Making, Fuzzy Set Theory and Aggregation Operators.