In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. Through this copula we can extend the Marshall-Olkin distribution in order to construct several bivariate survival functions. The cumulative distribution functions of these distributions are not absolute continuous functions and they unknown parameters are often not be obtained in explicit form. In particular we consider the IFM method to find the Marshall-Olkin copula estimator, presenting the copula likelihood function. We compare this procedure with a non parametric estimator of the copula, the bivariate empirical copula, used to evaluate the copula goodness of fit. The estimate procedures described are verified through several simulation. One data-set is analyzed for a illustrative purpose.

Osmetti, S. A., Parametric and non-parametric estimate of bivariate survival functions: the copula approach, in Conference proceeding of XLV Riunione Scientifica della Società Italiana di Statistica, (Padova, 16-18 June 2010), N/A, Padova 2010: 1-8 [http://hdl.handle.net/10807/19738]

### Parametric and non-parametric estimate of bivariate survival functions: the copula approach

#### Abstract

In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. Through this copula we can extend the Marshall-Olkin distribution in order to construct several bivariate survival functions. The cumulative distribution functions of these distributions are not absolute continuous functions and they unknown parameters are often not be obtained in explicit form. In particular we consider the IFM method to find the Marshall-Olkin copula estimator, presenting the copula likelihood function. We compare this procedure with a non parametric estimator of the copula, the bivariate empirical copula, used to evaluate the copula goodness of fit. The estimate procedures described are verified through several simulation. One data-set is analyzed for a illustrative purpose.
##### Scheda breve Scheda completa Scheda completa (DC)
2010
Inglese
Conference proceeding of XLV Riunione Scientifica della Società Italiana di Statistica
XLV scientific meeting of the Italian Statistical Society
16-giu-2010
18-giu-2010
978-88-6129-566-7
N/A
Osmetti, S. A., Parametric and non-parametric estimate of bivariate survival functions: the copula approach, in Conference proceeding of XLV Riunione Scientifica della Società Italiana di Statistica, (Padova, 16-18 June 2010), N/A, Padova 2010: 1-8 [http://hdl.handle.net/10807/19738]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/10807/19738`
• ND
• ND
• ND