In many scientific fields, researchers are concerned with multivariate random variables. Although quantities measured on a continuous scale are more frequent, nevertheless multivariate count data often arise in several contexts (statistical process control, epidemiology, failure and reliability analysis, etc). Such data are frequently modelled through the multivariate Poisson distribution, based on a general multivariate reduction scheme, which however suffers from some practical limits. Various methods have been proposed for constructing new alternative multivariate discrete random variables that can be used as viable alternatives. One of the most straightforward is that based on joining arbitrary univariate discrete distributions through a copula function; this method allows for both flexible dependence structure and flexible choice of margins. In this work, we discuss some bivariate geometric distributions derived according to different copula functions, examining their properties, with particular regard to reliability concepts, and fitting them to real datasets taken from the literature.

On bivariate copula-based geometric models with application to reliability / A. Barbiero - In: Balkan Conference on operational research : book of abstracts / [a cura di] M. Martić, G. Savić, M. Kuzmanović. - [s.l] : Ministry of Education, Science and Technological Development of the Republic of Serbia, 2018 May 27. - ISBN 9788680593654. - pp. 56-56 (( Intervento presentato al 13. convegno Balkan Conference on Operational Research tenutosi a Belgrade nel 2018.

On bivariate copula-based geometric models with application to reliability

A. Barbiero
Primo
2018

Abstract

In many scientific fields, researchers are concerned with multivariate random variables. Although quantities measured on a continuous scale are more frequent, nevertheless multivariate count data often arise in several contexts (statistical process control, epidemiology, failure and reliability analysis, etc). Such data are frequently modelled through the multivariate Poisson distribution, based on a general multivariate reduction scheme, which however suffers from some practical limits. Various methods have been proposed for constructing new alternative multivariate discrete random variables that can be used as viable alternatives. One of the most straightforward is that based on joining arbitrary univariate discrete distributions through a copula function; this method allows for both flexible dependence structure and flexible choice of margins. In this work, we discuss some bivariate geometric distributions derived according to different copula functions, examining their properties, with particular regard to reliability concepts, and fitting them to real datasets taken from the literature.
Copula; Correlated discrete variables; Failure rate; Geometric distribution; Reliability
Settore SECS-S/01 - Statistica
Mathematical Institute of the Serbian Academy of Sciences and Arts
Yugoslav Society for Applied and Industrial Mathematics
University of Belgrade
Society of Operations Researchers of Serbia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/580515
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