The aim of this paper is the derivation of the maximum likelihood estimators of the Marshal-Olkin copula. This copula comes from the Marshall-Olkin Bivariate Exponential (MOBE) distribution, that has been proposed in reliability analysis to study complex systems in which the components are not independent and it is also used in the extreme value theory. We find the likelihood estimators considering the cases of complete and Type-II censored samples. The Marshall-Olkin copula likelihood function is presented in both cases. A simulation study in the particular context of the MOBE shows the properties of the proposed estimators for full or censored data. Finally, we analyze some data sets for illustrative purpose.
Osmetti, S. A., MAXIMUM LIKELIHOOD ESTIMATE OF MARSHALL-OLKIN COPULA PARAMETER: COMPLETE AND CENSORED SAMPLE, <<STATISTICA APPLICATA>>, 2012; 2012 (N/A): 1-33 [http://hdl.handle.net/10807/18822]
MAXIMUM LIKELIHOOD ESTIMATE OF MARSHALL-OLKIN COPULA PARAMETER: COMPLETE AND CENSORED SAMPLE
Osmetti, Silvia Angela
2012
Abstract
The aim of this paper is the derivation of the maximum likelihood estimators of the Marshal-Olkin copula. This copula comes from the Marshall-Olkin Bivariate Exponential (MOBE) distribution, that has been proposed in reliability analysis to study complex systems in which the components are not independent and it is also used in the extreme value theory. We find the likelihood estimators considering the cases of complete and Type-II censored samples. The Marshall-Olkin copula likelihood function is presented in both cases. A simulation study in the particular context of the MOBE shows the properties of the proposed estimators for full or censored data. Finally, we analyze some data sets for illustrative purpose.
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